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Combinatorics and random matrix theory / Jinho Baik, Percy Deift and Toufic Suidan.

By: Contributor(s): Material type: TextTextSeries: Graduate studies in mathematics ; 172.Publication details: Providence : American Mathematical Society, ©2016.Description: xi, 461 pages : illustrations ; 26 cmISBN:
  • 9780821848418 (hbk. : acidfree paper)
Subject(s): DDC classification:
  • 511.6 23 B152
Contents:
1. Introduction -- 2. Poissonization and de-Poissonization -- 3. Permutations and Young tableaux -- 4. Bounds of the expected value of $\ell_N$ -- 5. Orthogonal polynomials, Riemann-Hilbert problems, and Toeplitz matrices -- 6. Random matrix theory -- 7. Toeplitz determinant formula -- 8. Fredholm determinant formula -- 9. Asymptotic results -- 10. Schur measure and directed last passage percolation 11. Determinantal point processes -- 12. Tiling of the Aztec diamond -- 13. The Dyson process and Brownian Dyson process -- Appendices.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 511.6 B152 (Browse shelf(Opens below)) Available 137954
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Poissonization and de-Poissonization --
3. Permutations and Young tableaux --
4. Bounds of the expected value of $\ell_N$ --
5. Orthogonal polynomials, Riemann-Hilbert problems, and Toeplitz matrices --
6. Random matrix theory --
7. Toeplitz determinant formula --
8. Fredholm determinant formula --
9. Asymptotic results --
10. Schur measure and directed last passage percolation
11. Determinantal point processes --
12. Tiling of the Aztec diamond --
13. The Dyson process and Brownian Dyson process --
Appendices.

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.

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