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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, March  7, 2019}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape Omri Sarig 
  %
  (Weizmann Institute)
}
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will talk about
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{\Large\bfseries Local limit theorem for inhomogeneous Markov chains (joint with Dolgopyat)\par}
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\textsc{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 the 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 $N\to\infty$. 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.








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