Simultaneous Asymptotics for the Shape of Young Tableaux: Tracy-Widom and beyond.

Series: 
Stochastics Seminar
Thursday, September 10, 2009 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Georgia Tech

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 corresponding random RSK Young tableaux are investigated, when both
n and m converge together to infinity. If m does not grow too fast and
if the draws are uniform, 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 random word, towards the Tracy-Widom distribution.