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 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.
2019 Dec 17

Nishant Chandgotia (HUJI), Predictive sets.

2:00pm to 3:00pm

Location: 

Ross 70
Abstract: A subset of the integers P is called predictive if for all zero-entropy processes X_i; i in Z, X_0 can be determined by X_i; i in P. The classical formula for entropy shows that the set of natural numbers forms a predictive set. In joint work with Benjamin Weiss, we will explore some necessary and some sufficient conditions for a set to be predictive. These sets are related to Riesz sets (as defined by Y. Meyer) which arise in the study of singular measures. This and several questions will be discussed during the talk.
2020 Jan 28

Benjamin Weiss (HUJI) On the construction of measure distal transformations

2:00pm to 3:00pm

Location: 

Ross 70

Abstract: I will explain what measure distal transformations are
and describe some new constructions obtained with Eli Glasner.
These answer, inter alia, a question recently raised by Ibarlucia and Tsankov
concerning the existence of strongly ergodic non compact distal actions of the
free group.
2019 Dec 03

Ilya Gekhtman (Toronto)

2:00pm to 3:00pm

Location: 

Ross 70
Gibbs measures vs. random walks in negative curvature
The ideal boundary of a negatively curved manifold naturally carries two types of measures.
On the one hand, we have conditionals for equilibrium (Gibbs) states associated to Hoelder potentials; these include the Patterson-Sullivan measure and the Liouville measure. On the other hand, we have stationary measures coming from random walks on the fundamental group.
2019 Dec 10

Boris Solomyak (BIU) Hoelder regularity for the spectrum of translation flows

2:00pm to 3:00pm


Abstract: We consider generic translation flows corresponding to Abelian differentials on flat surfaces of genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. Recently Forni obtained Hoelder estimates on spectral measures for almost all translation flows, following earlier work by Bufetov and myself in genus two. Combining Forni's idea with our methods, we extended our proof to the case of arbitrary genus $g\ge 2$. It is based on a vector form of the Erd\H{o}s-Kahane argument, which I will try to explain.
This is a joint work with A. Bufetov.
2019 Oct 29

Zemer Kosloff, Finitary isomorphisms of Brownian motions

2:00pm to 3:00pm

Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow and thus Ornstein theory yielded the existence of a measure-preserving isomorphism between any two such Brownian motions. For fixed h >0, we construct by elementary methods, isomorphisms with almost surely finite coding windows between Brownian motions reflected on the intervals [0, qh] for all positive rationals q. This is joint work with Terry Soo.
2019 Nov 19

Tom Meyerovitch (BGU), Efficient finitary codings by Bernoulli processes

2:00pm to 3:00pm

Abstract:
Recently Uri Gabor refuted an old conjecture stating that any
finitary factor of an i.i.d process is finitarly isomorphic to an
i.i.d process. Complementing Gabor's result,
in this talk, which is based on work in progress with Yinon Spinka,
we will prove that any countable-valued process which is admits a
finitary a coding by some i.i.d process furthermore admits an
$\epsilon$-efficient finitary coding, for any positive $\epsilon$.
Here an ``$\epsilon$-efficient coding'' means that the entropy

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