# Meeting Details

For more information about this meeting, contact Becky Halpenny.

Title: “Studies on the weak convergence of partial sums in Gibbs-Markov dynamical systems” Ph.D. Thesis Defense Xuan Zhang, Adviser: Manfred Denker, Penn State We investigates distributional limit theorems of partial sums of the form $f_{n,1}+f_{n,2}\circ T_n+\cdots+f_{n,n}\circ T_n^{n-1}$ for Gibbs-Markov dynamical systems $(X_n, \mathscr B_n, T_n,\mu_n,\alpha_n)$ and an array of functions $f_{n,m}: X_n\to \mathbb R$ of certain classes. We show a Central Limit Theorem (CLT) for this array, a CLT of Lindeberg type (with uniformly bounded functions) and we also investigate the Poisson limit case. We relate the Poisson limit theorem to escape rates of sweep-out sets and the CLT is applied in various situations, in particular to some statistical functions.

### Room Reservation Information

Room Number: MB114 03 / 05 / 2015 08:30am - 11:00am