# Ergodic Theory Meeting

#### Thursday 9th June

All talks will be in Room MS.03 in the Zeeman Building (Mathematics Institute).

Schedule

1:30pm-2:30pm **Michael Bromberg** (Bristol)

Title: *Bounded rational ergodicity of the cylinder map*

Abstract: Click here.

2:45pm-3:45pm **Peyman Eslami** (Warwick)

Title: *Coupling for piecewise expanding maps*

Abstract: I will explain the coupling method for 1D piecewise expanding maps of the interval. This is a method to obtain statistical properties of dynamical systems, in particular, decay of correlations. In comparison with other methods, it is more flexible and leads to explicit constants. In the past it has been applied to more complicated systems, e.g. billiards, but such systems also have more structure. Here we focus on 1D piecewise expanding maps but our goal is to devise a method that is flexible enough to be generalized to higher dimensional systems.

TEA

4:15pm-5:15pm** Damien Thomine** (Orsay)

Title: *Potential kernel, hitting probabilities and limit distributions*

Abstract: Abelian extensions of hyperbolic dynamical systems are a class of measure-preserving transformations which are useful to understand diffusion phenomena. The simplest examples are random walks on $\mathbb{Z}$ or $\mathbb{Z}^2$; this class also includes interesting examples with a more dynamical flavour, such as Lorentz' gases, which are $\mathbb{Z}$ or $\mathbb{Z}^2$-periodic convex billiard.

The goal of this work is to transpose in the context of $\mathbb{Z}^d$ extensions a result which is known for random walks, namely, the link between the potential kernel of the random walk (which is an elementary solution of the Poisson's equation associated with the transition kernel of the random walk) and the probability that an excursion hits a given point. We shall also show how to interpret this link using the limit distribution of a well-chosen process.

Joint work with Françoise Pène (Université de Bretagne Occidentale).

For people who arrive in time we will meet in the Common Room around 12:00 to go for lunch in University House (cafeteria style food). We will also go to a restaurant for dinner in the evening.

This is part of the LMS Scheme 3 funded network of collaborative meetings.