Asymptotics for random Young diagrams, a.k.a. asymptotics for last passage percolation along thin rectangles and dependent weights.

Stochastics Seminar
Thursday, September 8, 2011 - 15:05
1 hour (actually 50 minutes)
Skyles 006
School of mathematics, Georgia institute of Technology
Given a random word of size n whose letters are drawn independently from an ordered alphabet of size m, the fluctuations of the shape of the associated random RSK Young tableaux are investigated, when n and m converge together to infinity. If m does not grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau, i.e. of the length of the longest increasing subsequence of the word, towards the Tracy?Widom distribution.