The seminar meets on Tuesdays, 11:00-12:00, in 201

## This Week

### Asymptotic distributions for normalized ergodic sums over rotations

Let $x \to x+ \alpha$ be a rotation on the circle and let $\varphi$ be a function with bounded variation. Denote by $S_n(\varphi, x) := \sum_{j=0}^{n-1} \varphi(x+j \alpha)$ the ergodic sums.

For a large class of $\alpha$’s including irrationals with bounded partial quotients, we show decorrelation inequalities between the ergodic sums at time $q_k$, where the $q_k$’s are the denominators of $\alpha$.

This allows to study the asymptotic distribution of the ergodic sums $S_n(\varphi, x)$ after normalization, in particular for some step functions, along subsequences.

We will give also an application to a geometric model, the billiard flow in the plane with periodic rectangular obstacles when the flow is restricted to special directions.

## Fall 2017 meetings

### Upcoming Meetings

Date
Title
Speaker
Abstract
Nov 21 Asymptotic distributions for normalized ergodic sums over rotations Jean-Pierre Conze (Rennes)

Let $x \to x+ \alpha$ be a rotation on the circle and let $\varphi$ be a function with bounded variation. Denote by $S_n(\varphi, x) := \sum_{j=0}^{n-1} \varphi(x+j \alpha)$ the ergodic sums.

For a large class of $\alpha$’s including irrationals with bounded partial quotients, we show decorrelation inequalities between the ergodic sums at time $q_k$, where the $q_k$’s are the denominators of $\alpha$.

This allows to study the asymptotic distribution of the ergodic sums $S_n(\varphi, x)$ after normalization, in particular for some step functions, along subsequences.

We will give also an application to a geometric model, the billiard flow in the plane with periodic rectangular obstacles when the flow is restricted to special directions.

Nov 28 Ergodic theorems for random walks on locally compact groups Michael Lin (BGU)
Dec 5 TBA Oliver Sargent
Jan 9 TBA Jakub Konieczny (Hebrew University )

### Past Meetings

Date
Title
Speaker
Abstract
Oct 31 Operator ergodic theorems Michael Lin (BGU)

See attached file. This will be the first in a series of survey talks:

1. Operator ergodic theorems.

2. Ergodic and mixing theorems for Markov operators (discrete time Markov processes).

3. Ergodic theorems for random walks on locally compact groups (convolution powers). The second talk will focus on the results needed for the third one.

Nov 7 Markov Operators Michael Lin (BGU)

This is the second survey talk in the series. See attached file.