Combinatorics and Random Matrix Theory
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A01=Jinho Baik
A01=Percy Deift
A01=Toufic Suidan
Author_Jinho Baik
Author_Percy Deift
Author_Toufic Suidan
Category=PBD
Category=PBT
Category=PBV
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eq_isMigrated=2
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Product details
- ISBN 9780821848418
- Weight: 979g
- Dimensions: 178 x 254mm
- Publication Date: 30 Jun 2016
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
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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.
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.
Jinho Baik, University of Michigan, Ann Arbor, MI, USA.
Percy Deift, Courant Institute, New York University, NY, USA.
Percy Deift, Courant Institute, New York University, NY, USA.
