Simulation Study of the Length of Longest Increasing Subsequence of Finite Alphabets

Series: 
SIAM Student Seminar
Friday, November 20, 2009 - 13:00
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
Georgia Tech
Let X_1, X_2,...,X_n be a sequence of i.i.d random variables with values in a finite alphabet {1,...,m}. Let LI_n be the length of the longest increasing subsequence of X_1,...,X_n. We shall express the limiting distribution of LI_n as functionals of m and (m-1)- dimensional Brownian motions as well as the largest eigenvalue of Gaussian Unitary Ensemble (GUE) matrix. Then I shall illustrate simulation study of these results