We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.
This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.
Introduction Statement of the results Mixing time preliminaries Outline of the proof of Theorem 2.1 Random graph estimates Supercritical case Subcritical case Critical Case Fast mixing of the Swendsen-Wang process on trees Acknowledgements Bibliography
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.
This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic.
Examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.
The Women of the Wall are leading a groundbreaking struggle to gain the Israeli authorities' permission to pray according to their manner at Judaism's holiest prayer site, the Western Wall. This book is the first comprehensive academic study of their struggle, placing it in a comparative and theoretical context of wider religion-state conflicts and models.
Nira Yuval-Davis provides an authoritative overview and critique of writings on gender and nationhood, presenting an original analysis of the ways gender relations affect and are affected by national projects and processes. In Gender and Nation Yuval-Davis argues that the construction of nationhood involves specific notions of both `manhood′ and `womanhood′. She examines the contribution of gender relations to key dimensions of nationalist projects - the nation′s reproduction, its culture and citizenship - as well as to national conflicts and wars, exploring the contesting relations between feminism and nationalism. Gender and Nation is an important contribution to the debates on citizenship, gender and nationhood. It will be essential reading for academics and students of women′s studies, race and ethnic studies, sociology and political science.
What does police violence against minorities, or violent clashes between minorities and the police tell us about citizenship and its internal hierarchies? Indicative of deep-seated tensions and negative perceptions; incidents such as these suggest how minorities are vulnerable, suffer from or are subject to police abuse and neglect in Israel. Marked by skin colour, negatively stigmatized or rendered security threats, their encounters with police provide a daily reminder of their defunct citizenship. Taking as case studies the experiences and perceptions of four minority groups within Israel including Palestinian/Arab citizens, ultra-Orthodox Jews and Ethiopian and Russian immigrants, Ben-Porat and Yuval are able to explore different paths of citizenship and the stratification of the citizenship regime through relations with and perceptions of the police in Israel. Touching on issues such as racial profiling, police brutality and neighbourhood neglect, their study questions the notions of citizenship and belonging, shedding light on minority relationships with the state and its institutions.
This text fills the gaps in the research of nationality, regarding 'national education' in its double meaning: compulsory national education for all and creating opportunities for fostering national consciousness. The research deals with the Zionist period in (Eretz) Israel.
This book examines the place of women within ethnic and national communities in nine different societies, and the ways in which the state intervenes in their lives. Contributions from a group of scholars examine the situations in their religious, economic and historical context.
For many Israelis, it is the internecine conflict with the ultra-orthodox Haredim that impacts their lives the most. The majority of Haredim -- raised with an intense focus on religion at the expense of all else -- are unemployable in a modern economy. Many choose to pursue religious studies, which the government subsidizes up to the age of 40. The first book on a conflict that is fast crystallizing into a national debate, The War Within is a lively and trenchant exploration of a battle between church and state as it plays out before our eyes in Israel today. As acclaimed journalists Yuval Elizur and Lawrence Malkin expose, the situation today has reached a critical point that threatens the state of Israel from within and must certainly affect its future.
Refreshingly honest, fast-paced, and full of humor, The List is full of practical advice and inspiration that will help you achieve your goals. Already an international bestseller, the book began as a list of 10 things the author wanted to accomplish in 400 days. He posted the list on his blog and asked for help—and within 24 hours was overwhelmed by responses. The key idea is as simple as it is powerful—let others know about your dreams and they will help you achieve them. Why do some people succeed where others fail? What makes some push past their financial hardships while others lag behind? What is holding you back? Yuval Abramovitz provides thought-provoking true stories, tips, insights, and techniques to show readers how to move past roadblocks, ask and receive help, and reach even the loftiest of goals. The List is filled with exercises and prompts for lists that help you make your dreams a reality. The author’s journey—from writing his first list in a wheelchair to becoming a well-known author, cultural reporter, actor, and media personality—and the stories of people around the world using his method to achieve success prove that this is a motivational book that truly works.
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
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