Name: Combinatorics and Random Matrix Theory (en Inglés)
SKU: 67465840
Price: 175.39 USD
Availability: InStock
Author: Jinho Baik;Percy Deift;Toufic Suidan
ISBN: 9780821848418

portada Combinatorics and Random Matrix Theory (en Inglés)

Combinatorics and Random Matrix Theory (en Inglés)

Formato

Libro Físico

Editorial

American Mathematical Society

Autor

Jinho Baik;Percy Deift;Toufic Suidan

Colección

Graduate Studies in Mathematics

Año

2016

Idioma

Inglés

N° páginas

461

Encuadernación

Tapa Dura

Dimensiones

25.4x17.8 cm

ISBN13

9780821848418

Combinatorics and Random Matrix Theory (en Inglés)

Jinho Baik;Percy Deift;Toufic Suidan (Autor) · American Mathematical Society · Tapa Dura

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Reseña del libro "Combinatorics and Random Matrix Theory (en Inglés)"

The goal of this book is to analyse in detail 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. The book is self-contained, and develops enough of the theory from each area that a general reader can learn the subject directly from the text.

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.