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portada Combinatorics and Random Matrix Theory
Type
Physical Book
Publisher
Author
Collection
Graduate Studies in Mathematics
Year
2016
Language
English
Pages
461
Format
Hardcover
Dimensions
25.4x17.8 cm
ISBN13
9780821848418

Combinatorics and Random Matrix Theory

Jinho Baik;Percy Deift;Toufic Suidan (Author) · American Mathematical Society · Hardcover

Combinatorics and Random Matrix Theory - Jinho Baik;Percy Deift;Toufic Suidan

New Book Imported to Taiwan
Delivery: 22 Sep - 02 Oct Shipping: 11 to 14 business days.
NT$ 6,342
NT$ 6,342

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Synopsis "Combinatorics and Random Matrix Theory"

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.

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