Combinatorics and Random Matrix Theory (Hardcover)

Over the last fifteen years a variety of problems in combinatorics has been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a ``stochastic special function theory'' for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Graduate Studies in Mathematics
Release date:	February 2017
Authors:	Jinho Baik • Percy Deift • Toufic Suidan
Dimensions:	254 x 178 x 30mm (L x W x T)
Format:	Hardcover
Pages:	461
ISBN-13:	978-0-8218-4841-8
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
LSN:	0-8218-4841-0
Barcode:	9780821848418

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