Central Limit Theorem for Convex Sets

Probability Working Seminar
Friday, October 2, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 154
Stas Minsker – School of Mathematics, Georgia Tech
Yuri Bakhtin
The talk is based on the paper by B. Klartag. It will be shown that there exists a sequence \eps_n\to 0 for which the following holds: let K be a compact convex subset in R^n with nonempty interior and X a random vector uniformly distributed in K. Then there exists a unit vector v, a real number \theta and \sigma^2>0 such that d_TV(, Z)\leq \eps_n where Z has Normal(\theta,\sigma^2) distribution and d_TV - the total variation distance. Under some additional assumptions on X, the statement is true for most vectors v \in R^n.