Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the March enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U-statistics and Mm-estimators and develops their asymptotic properties. It also provides an elementary introduction to resampling, particularly in the context of these estimators. The last chapter is on practical implementation of the methods presented in other chapters, using the free software R.
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary multivariate analysis, basic time series analysis and basic results in stochastic convergence. Part I is on different methods of estimation of large covariance matrices and auto-covariance matrices and properties of these estimators. Part II covers the relevant material on random matrix theory and non-commutative probability. Part III provides results on limit spectra and asymptotic normality of traces of symmetric matrix polynomial functions of sample auto-covariance matrices in high-dimensional linear time series models. These are used to develop graphical and significance tests for different hypotheses involving one or more independent high-dimensional linear time series. The book should be of interest to people in econometrics and statistics (large covariance matrices and high-dimensional time series), mathematics (random matrices and free probability) and computer science (wireless communication). Parts of it can be used in post-graduate courses on high-dimensional statistical inference, high-dimensional random matrices and high-dimensional time series models. It should be particularly attractive to researchers developing statistical methods in high-dimensional time series models. Arup Bose is a professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in mathematical statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been editor of Sankhyā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His first book Patterned Random Matrices was also published by Chapman & Hall. He has a forthcoming graduate text U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee) to be published by Hindustan Book Agency. Monika Bhattacharjee is a post-doctoral fellow at the Informatics Institute, University of Florida. After graduating from St. Xavier's College, Kolkata, she obtained her master’s in 2012 and PhD in 2016 from the Indian Statistical Institute. Her thesis in high-dimensional covariance and auto-covariance matrices, written under the supervision of Dr. Bose, has received high acclaim.
In September 1600, Queen Elizabeth and London are made to believe that the East India Company will change England's fortunes forever. With William Shakespeare's death, the heart of Albion starts throbbing with four centuries of an extraordinary Indian settlement that Arup K. Chatterjee christens as Typogravia. In five acts that follow, we are taken past the churches destroyed by the fire of Pudding Lane; the late eighteenth-century curry houses in Mayfair and Marylebone; and the coming of Indian lascars, ayahs, delegates, students and lawyers in London. From the baptism of Peter Pope (in the year Shakespeare died) to the death of Catherine of Bengal; the chronicles of Joseph Emin, Abu Taleb and Mirza Ihtishamuddin to Sake Dean Mahomet's Hindoostane Coffee House; Gandhi's experiments in Holborn to the recovery of the lost manuscript of Tagore's Gitanjali in Baker Street; Jinnah's trysts with Shakespeare to Nehru's duels with destiny; Princess Sophia's defiance of the royalty to Anand establishing the Progressive Writers' Association in Soho; Aurobindo Ghose's Victorian idylls to Subhas Chandra Bose's interwar days; the four Indian politicians who sat at Westminster to the blood pacts for Pakistan; India in the shockwaves at Whitehall to India in the radiowaves at the BBC; the intrigues of India House and India League to hundreds of East Bengali restaurateurs seasoning curries and kebabs around Brick Lane... Indians in London is a scintillating adventure across the Thames, the Embankment, the Southwarks, Bloomsburys, Kensingtons, Piccadillys, Wembleys and Brick Lanes that saw a nation-a cultural, historical and literary revolution that redefined London over half a millennium of Indian migrations-reborn as independent India.
Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary multivariate analysis, basic time series analysis and basic results in stochastic convergence. Part I is on different methods of estimation of large covariance matrices and auto-covariance matrices and properties of these estimators. Part II covers the relevant material on random matrix theory and non-commutative probability. Part III provides results on limit spectra and asymptotic normality of traces of symmetric matrix polynomial functions of sample auto-covariance matrices in high-dimensional linear time series models. These are used to develop graphical and significance tests for different hypotheses involving one or more independent high-dimensional linear time series. The book should be of interest to people in econometrics and statistics (large covariance matrices and high-dimensional time series), mathematics (random matrices and free probability) and computer science (wireless communication). Parts of it can be used in post-graduate courses on high-dimensional statistical inference, high-dimensional random matrices and high-dimensional time series models. It should be particularly attractive to researchers developing statistical methods in high-dimensional time series models. Arup Bose is a professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in mathematical statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been editor of Sankhyā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His first book Patterned Random Matrices was also published by Chapman & Hall. He has a forthcoming graduate text U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee) to be published by Hindustan Book Agency. Monika Bhattacharjee is a post-doctoral fellow at the Informatics Institute, University of Florida. After graduating from St. Xavier's College, Kolkata, she obtained her master’s in 2012 and PhD in 2016 from the Indian Statistical Institute. Her thesis in high-dimensional covariance and auto-covariance matrices, written under the supervision of Dr. Bose, has received high acclaim.
Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the March enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Following an experimental railway track at Chintadripet, in 1835, the battle for India's first railroad was fought bitterly between John Chapman's Great Indian Peninsular Railway and Rowland MacDonald Stephenson's East India Railway Company, which was merged with Dwarkanauth Tagore's Great Western of Bengal Railway. Even at the height of the Mutiny of 1857, Bahadur Shah Zafar promised Indian owned railway tracks for native merchants if Badshahi rule was restored in Delhi. From Jules Verne to Rudyard Kipling to Mark Twain to Rabindranath Tagore to Nirad C. Chaudhuri to R.K. Narayan and Ruskin Bond-the aura of Indian trains and railway stations have enchanted many writers and poets. With iconic cinematography from The Apu Trilogy, Aradhana, Sonar Kella, Sholay, Gandhi, Dil Se, Parineeta, Barfi, Gangs of Wasseypur, and numerous others, Indian cinema has paved the way for mythical railroads in the national psyche. The Great Indian Railways takes us on a historic adventure through many junctions of India's hidden railway legends, for the first time in a book replete with anecdotes from imperial politics, European and Indian accounts, the battlefronts of the Indian nationalist movement, Indian cinema, songs, advertisements, and much more, in an ever-expanding cultural biography of the Great Indian Railways. Dubbed as 'one of a kind' this awe-inspiring saga is 'compulsive reading.' 'In this fascinating cultural history, Arup K Chatterjee charts the extraordinary journey of the Indian Railways, from the laying of the very first sleeper to the first post-Independence bogey. It evokes our collective accumulation of those innumerable memories of platform chai and rail-gaadi stories, bringing alive through myriad voices and tales the biography of one of India's defining public institutions.' – Shashi Tharoor, Author, M.P., Lok Sabha 'The Great Indian Railways is a fascinating and well-researched cultural biography of the Indian Railways-those intricate arteries of the soul of India, as have been experienced, written, filmed, and dreamed. We cannot all travel by rail to know India, as Gandhiji did, but we can and should read this book!' – Tabish Khair, Author, Professor
There has been, of late, a growing realisation that the pace and pattern of economic development of a country can hardly be understood and explained comprehensively in terms of the straitjacket of economics discipline alone. India is a prime example of the importance of the part played by a country's history, culture, sociology, and socio-cultural-religious norms, values, and institutions in its development process. This book, with its assorted essays of varying depths of scholarship and insightful reflections, attempts to drive home this point more forcefully than ever before. In its search for the non-economic roots of India’s overall sloth and murky progress in its broad-based economic and human development, the book illuminates major oddities deep inside a unique mental make-up full of perceptual and ideational dilemmas, many of which are arguably shaped by the long-lasting and dominant influence of what could be called the Brahminical lines of thinking and discourse. With India’s hazy and dodgy world of perceptions as a backdrop, the book also addresses – through its intelligent essays - the deep and sometimes dire ramifications of the historic advent and the dramatic advance of neoliberal market ideology today.
In September 1600, Queen Elizabeth and London are made to believe that the East India Company will change England's fortunes forever. With William Shakespeare's death, the heart of Albion starts throbbing with four centuries of an extraordinary Indian settlement that Arup K. Chatterjee christens as Typogravia. In five acts that follow, we are taken past the churches destroyed by the fire of Pudding Lane; the late eighteenth-century curry houses in Mayfair and Marylebone; and the coming of Indian lascars, ayahs, delegates, students and lawyers in London. From the baptism of Peter Pope (in the year Shakespeare died) to the death of Catherine of Bengal; the chronicles of Joseph Emin, Abu Taleb and Mirza Ihtishamuddin to Sake Dean Mahomet's Hindoostane Coffee House; Gandhi's experiments in Holborn to the recovery of the lost manuscript of Tagore's Gitanjali in Baker Street; Jinnah's trysts with Shakespeare to Nehru's duels with destiny; Princess Sophia's defiance of the royalty to Anand establishing the Progressive Writers' Association in Soho; Aurobindo Ghose's Victorian idylls to Subhas Chandra Bose's interwar days; the four Indian politicians who sat at Westminster to the blood pacts for Pakistan; India in the shockwaves at Whitehall to India in the radiowaves at the BBC; the intrigues of India House and India League to hundreds of East Bengali restaurateurs seasoning curries and kebabs around Brick Lane... Indians in London is a scintillating adventure across the Thames, the Embankment, the Southwarks, Bloomsburys, Kensingtons, Piccadillys, Wembleys and Brick Lanes that saw a nation-a cultural, historical and literary revolution that redefined London over half a millennium of Indian migrations-reborn as independent India.
Considering the acceleration of the Indian Higher Education sector’s digitalization due to the recent Covid-19 pandemic, this book entitled “Digital Transformation of Higher Education in India” aims to help academicians as well as library and information science professionals at all levels in India and globally to survive and thrive in the 21st century. ‘All levels’ include those in careers spread across all sectors of library and information work (such as local government, private or ‘special’ and academic libraries) and electronic information related posts such as webmasters and knowledge managers, Information Scientist.
In 1853 Karl Marx predicted the Indian Railways would foster the growth of parallel industries 'not immediately connected with the railways.' But the most successful industry-which Marx could not possibly have dreamed of-was that of cultural representations of the railways, which began even before the railways, themselves. From Rudyard Kipling to Mark Twain to R.K. Narayan to Ruskin Bond-the aura of Indian trains and railway stations have enchanted many. What imperialism made opulent, nationalism embraced a swadeshi tool, Partition turned into theaters of the macabre, and the nation's destiny marked for its favorite foster child, came to embody the portable architecture of India's modernity. And, what with iconic railway cinematography from Aradhana (1969), Sonar Kella (1974), Gandhi (1982), Dil Se (1997), or Parineeta (2005), Indian cinema has forged mythical railroads in the national psyche. The Purveyors of Destiny brings together all these elements together, for the first time, in a book replete with anecdotes from colonial and Indian accounts, the battlefronts of the Indian nationalist movement, Indian cinema, advertisements, and much more, in an ever expanding cultural biography of the Great Indian Railways. 'In this fascinating cultural history, Arup K Chatterjee charts the extraordinary journey of the Indian Railways, from the laying of the very first sleeper to the first post-Independence bogey. It evokes our collective accumulation of those innumerable memories of platform chai and rail-gaadi stories, bringing alive through myriad voices and tales the biography of one of India's defining public institutions.' – Shashi Tharoor, Author, M.P., Lok Sabha 'The Purveyors of Destiny is a fascinating and well-researched cultural biography of the Indian Railways-those intricate arteries of the soul of India, as have been experienced, written, filmed, and dreamed. We cannot all travel by rail to know India, as Gandhiji did, but we can and should read this book!' – Tabish Khair, Author, Professor 'Drawing on an impressive repertoire of literature and film, this elegantly crafted biography of the railways takes us on a riveting journey through the cultural history of the Indian nation, from the 1850s to the present. Written with wit and verve, it is a delight to read.' – Sugata Bose, Author, Professor, M.P., Lok Sabha 'A deeply engaging work that comfortably straddles, and masters, the worlds of academic research and modern nonfiction, offering countless delightful gems of India's railway legends and narratives for the curious reader. Crafted with great skill and a keen understanding of modern culture from the region and beyond...a remarkable achievement!' – Kaushik Barua, Author '...a wonderfully eclectic account of the Indian Railways and the vital place they occupy in our cultural history, with memorable moments and motifs from literature, cinema and other elements of our collective imagination. A great train journey, replete with all of the essentials from garam chai and A.H. Wheeler to historic arrivals and departures...' – Stephen Alter, Author
Adam’s Bridge offers the first comprehensive transdisciplinary study of the famous eponymous tombolo (also known as Ram Setu) combining its sacral, historical, geological, political, performative, and heritage aspects into one framework, viewed under the critical lenses of island studies and cultural theory. The book elucidates the entanglement of Adam’s Bridge’s discursive history with India’s colonial history, contemporary geology, domestic politics, and the nation’s emerging position in a complex geopolitical order in and around the Indian Ocean region, vis-à-vis increasing Sino-American involvement in Indo-Sri Lankan relations. Without foregrounding any absolute scientific claims on the location of the sandbars that inspired sage Valmiki’s Ram Setu and the Ramayan legacy or hindering narratives of religious faiths and folklore revolving around the structure, this intellectual historiography traces the parallel evolution of traditions of compassionate questioning and devotion for Indic sacred beliefs among commentators across the millennia from both Indian and non-Indian spectra, seen in juxtaposition with the biotic and abiotic diversity of the Gulf of Mannar and Palk Bay. Looking beyond secular-versus-religious debates, this book will be of interest to scholars of ocean and island studies, coastal economies, archipelagic geographies, environmental history, heritage studies, colonial studies, and cultural theory. Adam’s Bridge unifies a consortium of themes, ranging across ecological and livelihood sustainability, environmentalism, soteriology, economic and geostrategic history, and the United Nations Convention on the Law of the Sea, in conceptualizing a compellingly nuanced chronicle for India’s enchanted ‘bridge.’
This book examines various ideational, attitudinal and intellectual impasses that are becoming glaringly apparent on several fronts, and which have held back India’s balanced, steady and uniform development and transformation post-independence. It argues that all of these ideational and attitudinal aberrations stem from one basic fact, namely that India, throughout the entire period since the onset of modern industrial secular civilization at the global level, has somehow managed to evade the core ideas and values of the western Enlightenment movement, leaving unfinished the crucial task of modernizing and secularizing the mindsets and outlooks of its people on a mass scale – a task that has historically and globally been the backbone of sustained modern material development with socio-political stability. Further, it suggests that this enormous failure is crucially linked to key shortcomings in Indian mainstream thinking, and the imaginations and visions in general, and as such is also linked with confused educational ideas and content – particularly at the elementary level – since the country gained independence. The book maintains that Indian curricula and educational content at the school level has been consciously designed to guard against the core values and ideas of the Enlightenment, which could have made the typical Indian mind more rational, reasonable, mature and secular, resulting in much lower degrees of unreason, raw sentiments and emotions than have been hitherto entrenched in it. The book further sketches the genesis and impact of the currently dominant neoliberal ideas and thinking that have invaded the entire educational universe and its philosophy around the world. Lastly, it examines and assesses the latter’s far-reaching ramifications for current Indian educational philosophy, pedagogy and practices, and proposes concrete remedial directions for public policy and action.
Capitalism is in crisis today, while the neoliberal economic model that has been pursued in order to move out of the crisis has also not succeeded. There are also major disruptions in both economic and social polity, and uncertainties due to change and conflict within social relations. This book analyses these issues from a global perspective, with particular reference to India, in order to determine what can be done to provide this transitory situation with a direction of change. The essays gathered here counter the neo-liberal myth built on the premise that this is an era “free of ideology”, and reconstruct the concept of ideology and its various ramifications. The book also delves into how the dynamics of the overall economic situation today give rise to various possibilities for change, and details holistic plans of possible future actions.
What changes are occurring at the macro and the sectoral levels, how the labour market changes are taking place and what impact is felt on the low income households are some of the questions that the present volume focuses on. It begins by examining the sectoral composition of growth, revisiting the issues related to industry-services balance, and also brings out the spatial dimension of growth. On the one hand the industry does not seem to have played a major role in the context of employment generation as imported technology is by and large capital intensive in nature. On the other hand, the services-led growth is seen to have reduced the pace of poverty reduction. Given the services-led growth the possible impact of trade in services on employment both in the formal and informal sectors have been worked out, indicating limited positive spill-over effects. The labour market outcomes are brought out with great details suggesting that rapid economic growth in India could not result in productive employment generation on a large scale. The gender dimensions of employment are brought out to verify if reduction in labour market inequality can result in improving the position of women in other spheres encompassing the decision making process both within the household and outside the household. Issues relating to urbanisation and rural-urban migration are also covered to understand the dynamics of urban poverty and to bring out the challenges of population transfer given the spatial concentration of growth. The job search practices pursued by the low income households are often pursued in terms of informal networks. What problems are associated with such mechanisms in experiencing improvements in wellbeing levels are covered in the present volume. On the whole, the volume offers an explanation of limited poverty reduction in a situation of rapid economic growth on the basis of an inter-disciplinary framework though efforts are being made to keep the methodology quantitatively rigorous.
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