## “Bulletin Board”

School of Mathematics - November 10, 2007

### Short Course on

#### On the Hammersley Model with Applications to Combinatorics (6 Lectures)Fraydoun Rezakhanlou University of CaliforniaBerkeley, USA Nov. 22 - Dec. 12, 2007

On the Hammersley Model with Applications to Combinatorics (6 Lectures)
Fraydoun Rezakhanlou
University of California
Berkeley, USA
Nov. 22 - Dec. 12, 2007

Abstract

As a classical problem in combinatorics, consider the longest increasing subsequence of a random permutations of the sequence $1,2,\dots,n$. By a result of Vershik-Kerov and Logan-Shepp , the length of such a random subsequence $L_n$ is approximately $2\sqrt{n}$. Recently Baik, Deift and Johansson settled a long standing open problem by showing that the fluctuations of $L_n$ is of order $n^{1/6}$. In these lectures, I explain how probabilistic arguments can be used to study $L_n$. After the work of Hammerseley and Aldous-Diaconis, a random growth process known as Hammersely model is used to get insight into the behavior of $L_n$ as $n$ gets large.

Information

 Time and Date: Thursday, Nov. 22, 2007 - 16:00-18:00 Wednesday, Nov. 28, 2007 - 16:00-18:00 Sunday, Dec. 2, 2007 - 16:00-18:00 Wednesday, Dec. 5, 2007 - 16:00-18:00 Wednesday, Dec. 12, 2007 - 16:00-18:00 The date and time of 6th lecture will be announced.
Place: Lecture Hall, Niavaran Bldg., Niavaran Sqr., Tehran, Iran