Alice Guionnet's Books

Large random matrices

By: Alice Guionnet

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These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

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Page Count

296

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540698965

ISBN 13

9783540698968

An Introduction to Random Matrices

By: Greg W. Anderson,Alice Guionnet,Ofer Zeitouni

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An Introduction to Random Matrices

By: Greg W. Anderson,Alice Guionnet,Ofer Zeitouni

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

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Page Count

507

Publisher

Cambridge University Press

Published Date

ISBN 10

0521194520

ISBN 13

9780521194525

Asymptotic Expansion of a Partition Function Related to the Sinh-model

By: Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

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Asymptotic Expansion of a Partition Function Related to the Sinh-model

By: Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.

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Page Count

233

Publisher

Springer

Published Date

ISBN 10

3319333798

ISBN 13

9783319333793

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

By: Alice Guionnet

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Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

By: Alice Guionnet

Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.

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Page Count

154

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450275

ISBN 13

9781470450274

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

By: Alice Guionnet

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Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

By: Alice Guionnet

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Solve jigsaw puzzle

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Page Count

154

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450275

ISBN 13

9781470450274

Asymptotic Expansion of a Partition Function Related to the Sinh-model

By: Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

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Asymptotic Expansion of a Partition Function Related to the Sinh-model

By: Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

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N/A

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Solve jigsaw puzzle

Age

Page Count

233

Publisher

Springer

Published Date

ISBN 10

3319333798

ISBN 13

9783319333793

Book's by Alice Guionnet

Large random matrices

Large random matrices

An Introduction to Random Matrices

An Introduction to Random Matrices

Asymptotic Expansion of a Partition Function Related to the Sinh-model

Asymptotic Expansion of a Partition Function Related to the Sinh-model

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations

Asymptotic Expansion of a Partition Function Related to the Sinh-model

Asymptotic Expansion of a Partition Function Related to the Sinh-model

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