This book presents for the first time to a general readership recent groundbreaking developments in probability and combinatorics related to the longest increasing subsequence problem. Series: Institute of Mathematical Statistics Textbooks. Num Pages: 366 pages, 3 b/w illus. 94 exercises. BIC Classification: PBT. Category: (U) Tertiary Education (US: College). Dimension: 237 x 160 x 25. Weight in Grams: 628. . 2015. Illustrated. hardcover. . . . .

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Bibliographic Details

Title: The Surprising Mathematics of Longest Increasing Subsequences: 4 (Institute of Mathematical Statistics Textbooks, Series Number 4)
Publisher: Cambridge University Press
Publication Date: 2015
Language: English
ISBN 10: 1107075831
ISBN 13: 9781107075832
Binding: Hardcover
Condition: New

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Synopsis

In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists, and statisticians. The specific topics covered are the Vershik-Kerov–Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last 40 years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.

About the Author

Dan Romik is Professor of Mathematics at the University of California, Davis.

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