Dynamical & Probability

2019 Jan 01

Yotam Smilansky (HUJI), Multiscale substitution schemes and Kakutani sequences of partitions.

2:15pm to 3:15pm

Location: 

Ross 70
Abstract: Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which include the sequence of partitions of the unit interval considered by Kakutani as a special case. In this talk we will use new path counting results for directed weighted graphs to show that such sequences of partitions are uniformly distributed, thus extending Kakutani's original result. Furthermore, we will describe certain limiting frequencies
2018 Nov 27

Yan Dolinsky. A new type of stochastic target problems.

12:00pm to 1:00pm

Location: 

Coffee lounge
Abstract: I will discuss two stochastic target problem in the Brownian framework . The first problem has a nice solution which I will present. The second problem is much more complicated and for now remains open. I will discuss the challenges and connection with other fields in probability theory.
2019 Jan 15

Yeor Hafouta (HUJI) A local limit theorem for random dynamical systems.

2:15pm to 3:15pm

Location: 

Ross 70
Probabilistic limit theorems for (distance expanding and hyperbolic) dynamical systems is a well studied topic. In this talk I will present conditions guaranteeing that a local central limit theorem holds true for certain families of distance expanding random dynamical systems. If time permits, I will also discuss a version of the Berry-Esseen theorem. Joint work with Yuri Kifer.
2018 Dec 18

Matthew Foreman (UC IRVINE), Global Structure Theorems for the space of measure preserving transformations

2:15pm to 3:15pm

Abstract: This talk describes two classes of symbolic topological systems, the odometer based and the circular systems. The odometer based systems are ubiquitous--when equipped with invariant measures they form an upwards closed cone in the space of ergodic transformations (in the pre-ordering induced by factor maps). The circular systems are a small class, but represent the diffeomorphisms of the 2-torus built using the Anosov-Katok technique of approximation by conjugacy.
 
2018 Nov 27

Amir Dembo (Stanford), Large deviations of subgraph counts for sparse random graphs

2:15pm to 3:15pm

Location: 

Ross 70
For fixed t>1 and L>3 we establish sharp asymptotic formula for the log-probability that the number of cycles of length L in the Erdos - Renyi random graph G(N,p) exceeds its expectation by a factor t, assuming only that p >> log N/sqrt(N). In a narrower range of p=p(N) we obtain such sharp upper tail for general subgraph counts and for the Schatten norms of the corresponding adjacency matrices. In this talk, based on a joint work with Nick Cook, I will explain our approach, based on convex-covering and a new quantitative refinement of
2018 Dec 11

Demi Allen (Manchester) A mass transference principle for systems of linear forms with applications to Diophantine approximation

2:15pm to 3:15pm

Location: 

Ross 70
Abstract: In Diophantine approximation we are often interested in the Lebesgue and Hausdorff measures of certain $\limsup$ sets. In 2006, Beresnevich and Velani proved a remarkable result --- the Mass Transference Principle --- which allows for the transference of Lebesgue measure theoretic statements to Hausdorff measure theoretic statements for $\limsup$ sets arising from sequences of balls in $\mathbb{R}^k$.
2018 Nov 06

Jon Aaronson (TAU) On the bounded cohomology of actions of multidimensional groups.

2:15pm to 3:15pm

Although each cocycle for a action of the integers is specified by the sequence of Birkhoff sums of a function, it is relatively difficult to specify cocycles for the actions of multidimensional groups such as $\Bbb Z^2$. We'll see that if $(X,T)$ is a transitive action of the finitely generated (countable) group $\Gamma$ by homeomorphism of the polish space $X$, and $\Bbb B$ is a separable Banach space, there is a cocycle $F:\Gamma\times X \to\Bbb B$ with each $x\mapsto F(g,x)$ bounded and continuous so that the skew product action $(X x \Bbb B,S)$ is transitive where
2018 Dec 04

Dynamics Seminar: Omri Sarig (Weizmann) Local limit theorems for inhomogeneous Markov chains

2:15pm to 3:15pm

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 th 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—>infinity. 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.
2018 Oct 23

Dynamics Seminar: Nishant Chandgotia (HUJI). Some universal models for Z^d actions

2:15pm to 3:15pm

Location: 

Ross 70
Krieger’s generator theorem shows that any free invertible ergodic measure preserving action (Y,\mu, S) can be modelled by A^Z (equipped with the shift action) provided the natural entropy constraint is satisfied; we call such systems (here it is A^Z) universal. Along with Tom Meyerovitch, we establish general specification like conditions under which Z^d-dynamical systems are universal. These conditions are general enough to prove that 1) A self-homeomorphism with almost weak specification on a compact metric space (answering a question by Quas and Soo)
2018 Jun 26

Sieye Ryu (BGU): Predictability and Entropy for Actions of Amenable Groups and Non-amenable Groups

2:15pm to 3:15pm

Suppose that a countable group $G$ acts on a compact metric space $X$ and that $S \subset G$ is a semigroup not containing the identity of $G$. If every continuous function $f$ on $X$ is contained in the closed algebra generated by $\{sf : s \in S\}$, the action is said to be $S$-predictable. In this talk, we consider the following question due to Hochman: When $G$ is amenable, does $S$-predictability imply zero topological entropy? To provide an affirmative answer, we introduce the notion of a random invariant order.

Pages