Combinatorics and Random Matrix Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 172) - Hardcover

Jinho Baik; Percy Deift; Toufic Suidan

Hardcover

ISBN 10: 0821848410 ISBN 13: 9780821848418

Publisher: American Mathematical Society, 2016

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 this title

About the Author

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

Review

...[T]he book is carefully written and will serve as an excellent reference. --Terence Tao, Mathematical Reviews

The book covers exciting results and has a wealth of information. --Milós Bóna, MAA Reviews

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. --Zentralblatt MATH

Edition details

• Publisher: American Mathematical Society
• Publication date: 2016
• ISBN 10: 0821848410
• ISBN 13: 9780821848418
• Binding: Hardcover
• Language: English
• Number of pages: 461