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Dynamics Seminar: Omri Sarig (Weizmann) Local limit theorems for inhomogeneous Markov chains | Einstein Institute of Mathematics

Dynamics Seminar: Omri Sarig (Weizmann) Local limit theorems for inhomogeneous Markov chains

Date: 
Tue, 04/12/201814:15-15:15
Abstract: An inhomogeneous Markov chain X_n is a Markov chain whose state spaces and transition kernels change in time. A “local limit theorem” is an asymptotic formula for probabilities of th form
Prob[S_N-z_N\in (a,b)] , S_N=f_1(X_1,X_2)+....+f_N(X_N,X_{N+1})
in the limit N—>infinity. Here z_N is a “suitable” sequence of numbers.
I will describe general sufficient conditions for such results.
If time allows, I will explain why such results are needed for the study of certain problems related to irrational rotations.
This is joint work with Dmitry Dolgopyat.