The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics)

Science & Math

Zeitouni, Ofer

Anderson, Greg W.

Guionnet, Alice

Mathematics

Cambridge University Press

The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics, Series Number 118)

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.

Asymptotic Expansion of a Partition Function Related to the Sinh-model (Mathematical Physics Studies)

Borot, Gaëtan

Kozlowski, Karol K.

Reference

Springer

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.

Large Random Matrices: Lectures on Macroscopic Asymptotics: École d'Été de Probabilités de Saint-Flour XXXVI – 2006 (Lecture Notes in Mathematics, 1957)

Biane, Philippe: Non-commutative stochastic calculus. -Voiculescu, Dan-Virgil: Lectures on free probability. - Guionnet, Alice: Large random matrices: Lectures on macroscopic asymptotics.

Noncommutative Probability and Random Matrices at Saint-Flour (Probability at Saint-Flour)

Computers & Technology

Biane, Philippe

Voiculescu, Dan-Virgil

Software

See the best price to sell, buy, or rent books by Guionnet, Alice. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Guionnet, Alice