Dynamical & Probability

The Dynamics & Probability Seminar meets every Tuesday at 14:15 at Ross 70.
The HUJI dynamics group webpage can be found here.

2020 Jun 23

Dalia Terhesiu (Leiden) Mixing rates for Infinite horizon Lorentz maps

2:00pm to 3:00pm

Abstract: I will report on recent results on sharp error rates in the local limit theorem for the Sinai billiard map (one and two dimensional) with infinite horizon. This is joint work with F. Pene. This result allows to also obtain higher order terms and thus, sharp mixing rates in the speed of mixing of dynamically Hölder observables for the planar and tubular infinite horizon Lorentz gases in the map (discrete time) case.

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Meeting ID: 917 3652 5930
Password: 7m913h
2020 Jun 16

John Griesmer (Colorado School of Mines) Separating Bohr denseness from measurable recurrence

2:00pm to 3:00pm

Abstract: We construct a set which is dense in the Bohr topology on the group of integers and which is not a set of measurable recurrence, answering a question asked by Bergelson, Hegyvári, Ruzsa, and the author, in various combinations.  This talk will provide a broad overview and explain details of the construction. We will see similarities to many other examples in additive combinatorics and ergodic theory, such as Igor Kriz's construction showing topological recurrence does not imply measurable recurrence, and Ruzsa's niveau sets.
2020 Jun 09

Weikun He (HUJI), Equidistribution of linear random walks on the torus.

2:00pm to 3:00pm


Abstract: Quantitative equidistribution for linear random walks on the torus was first obtained by Bourgain, Furman, Lindenstrauss and Mozes. In this talk I will present a recent progress where the proximality assumption in their result is relaxed. I will also discuss an application to expansion in groups. This is based on a joint work with Nicolas de Saxcé.

Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=3c855e5a-44bf...
2020 May 26

Jon Aaronson (TAU) On mixing properties of infinite measure preserving transformations

2:00pm to 3:00pm

Abstract: I'll discuss  various  "ratio mixing"  properties
of transformations preserving infinite measures e.g. "Krickeberg mixing" (based on the example in Hopf's 1936 book) & "rational weak mixing". I'll also introduce a new one connected to "tied down" renewal theory.

Contains joint works with Hitoshi Nakada, Dalia Terhesiu & Toru Sera


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Meeting ID: 944 0148 4601
Password: 8w24u0
2020 Jun 02

Dynamics seminar : Rhiannon Dougall (Bristol) Critical exponents for subgroups of isometries of negatively curved spaces

2:00pm to 3:00pm


Abstract: One of the first things we learn about a (proper) Gromov hyperbolic geodesic space X is the construction of the visual boundary of X. An ergodic theorist then learns that for a non-elementary discrete group of isometries G acting properly on X, there is an interesting family of \delta_G-quasi-conformal measures on the boundary. The parameter \delta_G is called the critical exponent of G, and is equal to the exponential growth rate of the orbit Gx in X.
2020 May 05

Dynamics Seminar: Matan Seidel (TAU): "Random Walks on Circle Packings"

2:00pm to 3:00pm

Abstract: A circle packing is a canonical way of representing a planar graph. There is a deep connection between the geometry of the circle packing and the proababilistic property of recurrence/transience of the simple random walk on the underlying graph, as shown in the famous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However, by using certain natural weights that arise from the circle packing for a weighted random walk, (at least) one of the directions of the He-Schramm Theorem remains true.
2020 Apr 21

Tomasz Downarowicz (Wroclaw) Multiorder in countable amenable groups; a promising new tool in entropy theory.

2:00pm to 3:00pm

Location: 

E-seminar Zoom meeting ID 914-412-92758
Abstract: Let G be a countable group. A mutliorder is a collection of 
bijections from G to Z (the integers) on which G acts by a special 
"double shift". If G is amenable, we also require some uniform Folner 
property of the order intervals. The main thing is that mutiorder exists 
on every countable amenable group, which can be proved using tilings.
For now, multiorder provides an alternative formula for entropy of a 
process and we are sure in the nearest future it will allow at produce 
2020 Mar 24

Matan Seidel (TAU) Random walks on circle packings

2:00pm to 3:00pm

Abstract: A circle packing is a canonical way of representing a planar graph. There is a deep connection between the geometry of the circle packing and the proababilistic property of recurrence/transience of the simple random walk on the underlying graph, as shown in the famous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However, by using certain natural weights that arise from the circle packing for a weighted random walk, (at least) one of the directions of the He-Schramm Theorem remains true.
2019 Dec 25

Special dynamics seminar: Asaf Katz (Chicago) - Measure rigidity of Anosov flows via the factorization method

1:30pm to 3:30pm

Location: 

Ross 70
Title - Measure rigidity of Anosov flows via the factorization method.


Abstract: Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a Riemann surface.

In the talk we will introduce those flows and their dynamical behavior.
Moreover, we show how the factorization method, pioneered by Eskin and Mirzakhani in their groundbreaking work about measure rigidity for the moduli space of translation surfaces, can be adapted to smooth ergodic theory and in particular towards the study of Anosov flows.
2019 Dec 31

Mike Hochman (HUJI) Equidistribution for toral endomorphisms

2:00pm to 3:00pm

Location: 

Ross 70

Abstract: Host proved a strengthening of Rudolph and Johnson's measure rigidity theorem: if a probability measure is invariant, ergodic and has positive entropy for the map x2 mod 1, then a.e. point equidisitrbutes under x3 mod 1. Host also proved a version for toral endomorphisms, but its hypotheses are in some ways too strong, e.g. it requires one of the maps to be expanding, so it does not apply to pairs of  automorphisms. In this talk I will present an extension of Host's result (almost) to its natural generality.
2019 Dec 24

Dor Elimelech (BGU) Restricted permutations and perfect matchings

2:30pm to 3:30pm

Abstract:
A restricted permutation of a locally finite directed graph $G=(V,E)$ is a vertex permutation $\pi: V\to V$ for which $(v,\pi(v))\in E$, for any vertex $v\in V$. The set of such permutations, denoted by $\Omega(G)$, with a group action induced from a subset of graph isomorphisms form a topological dynamical system. In the particular case presented by Schmidt and Strasser (2016), where $V=\mathbb{Z}^d$ and $(n,m)\in E$ iff $(n-m)\in A$ ($A\subseteq \mathbb{Z^d}$ is fixed), $\Omega(G)$ is a subshift of finite type.

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