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Catalogue Information
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Details
Dewey Class
511.6
Title
Combinatorics and random matrix theory (M) / Jinho Baik, Percy Deift, Toufic Suidan
Author
Baik, Jinho, , 1973-
Added Personal Name
Deift, Percy, , 1945-
Suidan, Toufic , 1975-
Publication
Providence, Rhode Island : American Mathematical Society , 2016
Physical Details
xi, 461 pages : ill. ; 26 cm.
Series
Graduate studies in mathematics
; 172
ISBN
9780821848418
Summary Note
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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Subject References:
Random matrices
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Authors:
Baik, Jinho, 1973-
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Deift, Percy, 1945-
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Suidan, Toufic 1975-
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Series:
Graduate studies in mathematics
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Classification:
511.6
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0000000044470
519.21 BAI
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