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

Stochastics Seminar
Thursday, September 10, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 269
Christian Houdr̩ РGeorgia Tech
Yuri Bakhtin

Please Note: 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.