The Surprising Mathematics of Longest Increasing Subsequences

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.

Author: Dan Romik
Publisher: Cambridge University Press
Published: 02/02/2015
Pages: 366
Binding Type: Hardcover
Weight: 1.40lbs
Size: 9.10h x 6.20w x 1.00d
ISBN: 9781107075832

Review Citation(s):
Choice 12/01/2015

About the Author
Romik, Dan: - Dan Romik is Professor of Mathematics at the University of California, Davis.