Series: Graduate Studies in Mathematics. Num Pages: 461 pages, illustrations. BIC Classification: PBD; PBT; PBV. Category: (G) General (US: Trade). Dimension: 428 x 188 x 30. Weight in Grams: 982. . 2016. Hardcover. . . . .

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Bibliographic Details

Title: Combinatorics and Random Matrix Theory (Graduate Studies in Mathematics)
Publisher: American Mathematical Society
Publication Date: 2016
Language: English
ISBN 10: 0821848410
ISBN 13: 9780821848418
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

About the Author

Jinho Baik, University of Michigan, Ann Arbor, MI, USA. Percy Deift, Courant Institute, New York University, NY, USA.

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