As a consequence of certain independent developments in mathematics inrecent years, a wide variety of problems in combinatorics, some of long stand-ing, can now be solved in terms of random matrix theory (RMT). The goalof this book is to describe in detail these developments and some of theirapplications to problems in combinatorics. The book is based on courses ontwo key examples from combinatorial theory, viz., Ulam’s increasing sub-sequence problem, and the Aztec diamond. These courses were given atthe Courant Institute and the University of Michigan by two of the authors(P.D. and J.B., respectively) some ten years ago.The authors are pleased to acknowledge the suggestions, help, and infor-mation they obtained from many colleagues: Eitan Bachmat, Gerard BenArous, Alexei Borodin, Thomas Kriecherbauer, Eric Nordenstam, AndrewOdlyzko, Eric Rains, Raghu Varadhan, and Ofer Zeitouni. In particular,Eitan Bachmat and Thomas Kriecherbauer took on the task of reading themanuscript in full, catching typos, and suggesting many very helpful changesto the text. The authors would also like to acknowledge the support of NSFover the years when this book was written in the form of Grants DMS-0457335, DMS-0757709, DMS-1068646, and DMS-1361782 for J.B., DMS-0500923, DMS-1001886, and DMS-1300965 for P.D., and DMS-0553403 andDMS-0202530 for T.S. The first author (J.B.) and the third author (T.S.)would, in addition, like to acknowledge the support of an AMS Centen-nial Fellowship (2004–2005) and a Sloan Research Fellowship (2008-2010),respectively.

Combinatorics and Random Matrix Theory PDF

The list of books you might like