tag:www.math.bgu.ac.il,2005:/en/research/seminars/pet/meetingsBGU Probability and ergodic theory (PET)2016-02-26T08:41:48+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/1202016-02-26T08:41:48+02:002016-04-19T20:58:54+03:00<span class="mathjax">Nishant Chandgotia: Entropy Minimality and Four-Cycle Free Graphs</span>October 27, 10:50—12:00, 2015, Math -101<div class="mathjax"><p>A topological dynamical system (X,T) is said to be entropy minimal if
all closed T-invariant subsets of X have entropy strictly less than
(X,T). In this talk we will discuss the entropy minimality of a
class of topological dynamical systems which appear as the space of
graph homomorphisms from Z^d to graphs without four cycles; for
instance, we will see why the space of 3-colourings of Z^d is entropy
minimal even though it does not have any of the nice topological
mixing properties.</p></div>Nishant Chandgotiahttps://sites.google.com/site/nishantchandgotia/Tel Avivtag:www.math.bgu.ac.il,2005:MeetingDecorator/1022016-02-26T08:33:39+02:002016-04-19T20:58:54+03:00<span class="mathjax">Sebastián Donoso: Topological structures and the pointwise convergence of some multiple averages for commuting transformations</span>November 3, 10:50—12:00, 2015, Math -101<div class="mathjax"><p>``Topological structures’’ associated to a topological dynamical system are recently developed tools in topological dynamics. They have several applications, including the characterization of topological dynamical systems, computing automorphisms groups and even the pointwise convergence of some averages. In this talk I will discuss some recent developments of this subject, emphasizing applications to the pointwise convergence of some averages.</p></div>Sebastián DonosoUniversidad de Chile/ Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/1062016-02-26T08:33:39+02:002016-04-19T20:58:54+03:00<span class="mathjax">Yunied Puig de Dios: A mixing operator T for which (T, T^2) is not disjoint transitive</span>November 10, 10:50—12:00, 2015, Math -101<div class="mathjax"><p>Using a result from Ergodic Ramsey theory, we answer a question posed by Bès, Martin, Peris and Shkarin by showing a mixing operator $T$ on a Hilbert space such that the tuple $(T, T^2)$ is not disjoint transitive.</p></div>Yunied Puig de DiosBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/892016-02-26T07:30:25+02:002016-04-19T20:58:54+03:00<span class="mathjax">Mira Shamis: Applications of discrete Schroedinger equations to the standard map</span>December 8, 10:50—12:00, 2015, Math -101<div class="mathjax">
<p>We shall discuss the Chirikov standard map, an area-preserving
map of the torus to itself in which quasi-periodic and chaotic dynamics
are believed to coexist. We shall describe how the problem can be related
to the spectral properties of a one-dimensional discrete Schroedinger
operator, and present a recent result. Based on joint work with T. Spencer.</p></div>Mira ShamisWeizmanntag:www.math.bgu.ac.il,2005:MeetingDecorator/922016-02-26T07:30:25+02:002016-04-19T20:58:54+03:00<span class="mathjax">Izhar Oppenheim: Strengthening of Banach property (T) and applications</span>December 15, 10:50—12:00, 2015, Math -101<div class="mathjax">
<p>Property (T) was introduced by Kazhdan in 1967 as a way to establish compact generation of groups and since then was found useful for many other applications such as group cohomology and expander graphs.
I will introduce a new notion of property (T) in Banach spaces, present a criterion for the fulfillment of this property and discuss its applications to the construction of Banach expanders and to group fix point properties in Banach spaces.</p></div>Izhar Oppenheimhttps://sites.google.com/site/izharo/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/952016-02-26T07:30:25+02:002016-04-19T20:58:54+03:00<span class="mathjax">Guy Cohen: REMARKS ON RATES OF CONVERGENCE OF POWERS OF CONTRACTIONS</span>December 22, 10:50—12:00, 2015, Math -101<div class="mathjax"><p>We prove that if the numerical range of a Hilbert space contraction
$T$ is in a certain closed convex set of the unit disk which touches the unit
circle only at 1, then $|T^n(I-T)| =\mathcal O(1/n^{\beta})$ with
$\beta \in [\frac{1}{2}, 1)$.
For normal contractions the condition is also necessary.
Another sufficient condition for $\beta=\frac{1}{2}$, necessary for $T$ normal,
is that the numerical range of $T$ be in a disk
${z: |z-\delta| \le 1-\delta}$ for some $\delta \in (0,1)$.
As a consequence of results of Seifert, we obtain that a power-bounded
$T$ on a Hilbert space satisfies $|T^n(I-T)| = \mathcal O(1/n^{\beta})$
with $\beta \in (0,1]$ if and only if
$\sup_{1<|\lambda| <2} |\lambda -1|^{1/\beta} |R(\lambda,T)|< \infty$.
When $T$ is a contraction on $L_2$ satisfying the numerical range
condition, it is shown that $T^nf /n^{1-\beta}$ converges to 0 a.e.
with a maximal inequality, for every $f \in L_2$. An example shows
that in general a positive contraction $T$ on $L_2$ may have an
$f \ge 0$ with $\limsup T^nf/\log n \sqrt{n} =\infty$ a.e.</p></div>Guy Cohenhttp://www.ee.bgu.ac.il/~guycohen/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/982016-02-26T07:30:25+02:002016-04-19T20:58:54+03:00<span class="mathjax">Ron Rosenthal: Local limit theorem for strongly ballistic random walk in random environments</span>December 29, 10:50—12:00, 2015, Math -101<div class="mathjax">
<p>We study the model of random walk in random environments in dimension four and higher under Sznitman’s ballisticity condition (T’). We prove a version of a local Central Limit Theorem for the model and also the existence of an equivalent measure which is invariant with respect to the point of view of the particle. This is a joint work with Noam Berger and Moran Cohen.</p></div>Ron Rosenthalhttps://sites.google.com/site/ronrosenthal01/ETH Zurichtag:www.math.bgu.ac.il,2005:MeetingDecorator/802016-02-26T07:29:44+02:002016-10-11T21:19:54+03:00<span class="mathjax">Zemer Kosloff: Relative complexity of random walks in random sceneries in the absence of a weak invariance principle for local times</span>January 5, 10:50—12:00, 2016, Math -101Zemer Kosloffhttps://www.math.bgu.ac.il///www2.warwick.ac.uk/fac/sci/maths/people/staff/zemer_kosloff/Warwicktag:www.math.bgu.ac.il,2005:MeetingDecorator/1472016-04-07T13:33:12+03:002016-04-19T20:58:54+03:00<span class="mathjax">Yair Glasner: On isolated subgroups and generic permutation representations.</span>April 12, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>The subspace Sub(G) of all subgroups of a countable group G admits a natural structure of a compact metrizable space called the Chabauty space of G. What does the topological structure of the Chabauty space tell us about the algebraic structure of the group G?</p>
<p>A subgroup of Sub(G) is called isolated if it corresponds to an isolated subgroup of G. Isolated subgroups are very special from an algebraic point of view. A group G is called solitary if the isolated points are dense in Sub(G). I will show how the solitary condition is reflected in a surprising way in the permutation representation theory of G. And show how for finitely generated groups the notion of solitary groups generalizes the notion of LERF (subgroup separable) groups.</p>
<p>The talk is based on a joint work with Daniel Kitroser and Jullien Melleray.</p></div>Yair Glasnerhttps://www.math.bgu.ac.il/~yairgl/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1492016-04-30T23:24:00+03:002016-04-30T23:24:01+03:00<span class="mathjax">Ariel Yadin: The critical point for percolation on groups</span>May 3, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>I will discuss a conjecture of Benjamini & Schramm from 1996:
Any Cayley graph has a non-trivial critical point for percolation (i.e. p_c<1) unless the underlying group is a I finite extension of Z.</p>
<p>I will try to present a strategy to prove this conjecture (in fact some stronger form of it), that involves the notion of EIT = exponential intersection tail measures.
Hopefully, all the notions involved (percolation, the critical point p_c, EIT, etc.) will be explained.
The aim is to learn these notions and perhaps discuss the weakness or plausibility of the strategy proposed.</p></div>Ariel YadinBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1572016-06-19T15:11:07+03:002016-06-19T15:11:07+03:00<span class="mathjax">Naomi Feldheim: Mean and Minimum</span>June 21, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>Let X and Y be two unbounded positive independent random variables. Write Min_m for the probability of the event {min(X,Y) > m} and Mean_m for that of the event {(X+Y)/2 > m}. We show that the limit inferior of Min_m / Mean_m is always 0 (as m approaches infinity), regardless of the distributions of X and Y. We view this statement as a universal anti-concentration result, and discuss several implications. The proof is elementary but involved, relying on comparison to the “nearest” log-concave measure. We also provide a multiple-variables, weighted variant of this result in the i.i.d. case and pose a conjectured general result encompassing this phenomenon.
Joint work with Ohad Feldheim</p></div>Naomi Feldheimhttp://web.stanford.edu/~naomifel/ Stanford tag:www.math.bgu.ac.il,2005:MeetingDecorator/1592016-09-11T15:19:31+03:002016-10-09T23:43:59+03:00<span class="mathjax">Jean-Pierre Conze: Remarks on the set of values of the ergodic sums of an integer valued function</span>November 8, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>For an ergodic measure preserving dynamical system $(X, \cal B, \mu, T)$ and a measurable function $f$ with values in $\mathbb{Z}$, we consider for $x \in X$ the set of values of the ergodic sums $S_nf(x):= \sum_0^{n-1} f(T^k x), n \geq 1$.</p>
<p>If $f$ is integrable with $\mu(f) > 0$, several properties of this set (from the point of view of recurrence or arithmetic sets) are simple consequences of Bourgain’s results (1989).</p>
<p>For example, the set ${S_nf(x), n \geq 1}$ contains infinitely many squares for a.e. $x$. If $f$ is not integrable, this property may fail, as shown by a construction of M. Boshernitzan. We give also a counter-example of an integrable centered function $f$ for which the cocycle $(S_nf(x), n \geq 1)$ is non regular and the property fails.</p></div>Jean-Pierre Conzehttps://perso.univ-rennes1.fr/jean-pierre.conze/Rennestag:www.math.bgu.ac.il,2005:MeetingDecorator/1682016-10-13T10:40:28+03:002016-10-13T10:40:29+03:00<span class="mathjax">Sieye Ryu: Conjugacy invariants of a $D_{\infty}$-Topological Markov chain</span>November 22, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>Time reversal symmetry arises in many dynamical systems. In particular, it is an important aspect of dynamical systems which emerge from physical theories such as classical mechanics, thermodynamics and quantum mechanics. In this talk, we introduce the notion of a reversible dynamical system in symbolic dynamics. We investigate conjugacy invariants of a topological Markov chain which possesses an involutory reversing symmetry.</p></div>Sieye RyuBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2032016-12-01T16:45:38+02:002016-12-04T09:32:19+02:00<span class="mathjax">Sebastien Martineau: The geometry of locally infinite graphs</span>December 6, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>The geometry of graphs is usually studied in the locally finite setup: each vertex has finitely many neighbors. By compactness arguments, one proves some useful and classical regularity theorems for such graphs. Such theorems are easily disproved for locally infinite graphs, but finding homogeneous counter-examples (transitive or Cayley) leads to interesting constructions. I will explain why the geometry of locally infinite graphs is worth studying, present my results, and state some questions I currently cannot answer.</p></div>Sebastien MartineauWeizmanntag:www.math.bgu.ac.il,2005:MeetingDecorator/1752016-10-17T21:17:43+03:002016-11-08T08:06:03+02:00<span class="mathjax">Yair Hartman: Percolation, Invariant Random Subgroups and Furstenberg Entropy</span>December 11, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>In this talk I’ll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.</p>
<p>All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.</p></div>Yair Hartmanhttp://www.math.northwestern.edu/~hartman/Northwestern Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2052016-12-03T21:47:07+02:002016-12-03T21:47:07+02:00<span class="mathjax">Raimundo Briceño: New techniques for pressure approximation in Z^d shift spaces</span>December 20, 10:50—12:00, 2016, Math -101<div class="mathjax"><p>Given a Z^d shift of finite type and a nearest-neighbour interaction, we present sufficient conditions for efficient approximation of pressure and, in particular, topological entropy. Among these conditions, we introduce a combinatorial analog of the measure-theoretic property of Gibbs measures known as strong spatial mixing and we show that it implies many desirable properties in the context of symbolic dynamics. Next, we apply our results to some classical 2-dimensional statistical mechanics models such as the (ferromagnetic) Potts, (multi-type) Widom-Rowlinson, and hard-core lattice gas models for certain subsets of both the subcritical and supercritical regimes. The approximation techniques make use of a special representation theorem for pressure that may be of independent interest.</p>
<p>Part of this talk is joint work with Stefan Adams, Brian Marcus, and Ronnie Pavlov.</p></div> Raimundo Briceñohttps://sites.google.com/site/raimundob/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2252017-01-08T16:42:24+02:002017-01-16T16:33:16+02:00<span class="mathjax">Tom Meyerovitch: Entropy, Asymptotic pairs and Pseudo-Orbit Tracing for actions of amenable groups</span>January 17, 10:50—12:00, 2017, Math -101<div class="mathjax"><p>Chung and Li [Invent. Math. 2015] proved that for every expansive action of a countable polycyclic-by-finite group
<span class="kdmath">$\Gamma$</span> on a compact group <span class="kdmath">$X$</span> by continuous group automorphisms, positive entropy
implies the existence of non-diagonal asymptotic pairs.
In the same paper they asked if the this holds in general for an expansive action of a countable
amenable group <span class="kdmath">$\Gamma$</span> on a compact space <span class="kdmath">$X$</span>.</p>
<p>In my talk I plan to explain the notions involved Chung and Li’s question and discuss a property of dynamical systems called the ``pseudo-orbit tracing property’’. R. Bowen introduced the pseudo-orbit tracing property in the 1970’s for <span class="kdmath">$\mathbb{Z}$</span>-actions while studying Axiom A maps. I will prove that Chung and Li’s question has an affirmative answer if one also assumes pseudo-orbit tracing, and explain implications for algebraic actions (automorphisms of compact abelian groups).</p>
<p>I will also explain why the answer to Chung and Li’s question is negative if one doesn’t assume the pseudo-orbit tracing property, even when the acting group is <span class="kdmath">$\mathbb{Z}$</span>, or when the action is algebraic (but not both).</p></div>Tom Meyerovitchtag:www.math.bgu.ac.il,2005:MeetingDecorator/2132016-12-18T11:42:52+02:002016-12-18T11:42:52+02:00<span class="mathjax">Erez Nesharim: Diophantine approximation in function fields</span>February 28, 10:50—12:00, 2017, Math -101<div class="mathjax"><p>Irrational rotations of the circle <span class="kdmath">$T:\mathbb{R}/\mathbb{Z}\to \mathbb{R}/\mathbb{Z}$</span> are amongst the most studied dynamical systems. Rotations by badly approximable angels are exactly those for which the orbit of zero do not visit certain shrinking neighborhoods of zero, namely, there exists c>0 such that
<span class="kdmath">$T^n(0)\notin B\left(0,\frac{c}{n}\right)$</span> for all n.
Khinchine proved that every orbit of any rotation of the circle misses a shrinking neighborhood of some point of the circle. In fact, he proved that the constant of these shrinking neighborhoods may be taken uniformly. The largest constant, however, remains unknown.</p>
<p>We will introduce the notion of approximation by rational functions in the field <span class="kdmath">$\mathbb{F}_q((t-1)) ,$</span> formulate the analogue of Khinchine’s theorem over function fields and calculate the largest constant in this context.</p></div>Erez NesharimUniversity of Yorktag:www.math.bgu.ac.il,2005:MeetingDecorator/2642017-04-18T11:41:57+03:002017-04-19T10:05:49+03:00<span class="mathjax">Matthew Tointon: Approximate groups and applications to the growth of groups</span>April 25, 10:50—12:00, 2017, Math -101<div class="mathjax"><table>
<tbody>
<tr>
<td>Given a set A in a group, write $A^n$ for the set of all products $x_1…x_n$ with each $x_i$ belonging to A. Roughly speaking, a set A for which $A^2$ is “not much larger than” A is called an “approximate group”. The “growth” of A, on the other hand, refers to the behaviour of $</td>
<td>A^n</td>
<td>$ as n tends to infinity. Both of these have been fruitful areas of study, with applications in various branches of mathematics.</td>
</tr>
</tbody>
</table>
<p>Remarkably, understanding the behaviour of approximate groups allows us to convert information $A^k$ for some single fixed k into information about the sequence $A^n$ as n tends to infinity, and in particular about the growth of A.</p>
<table>
<tbody>
<tr>
<td>In this talk I will present various results describing the algebraic structure of approximate groups, and then explain how to use these to prove new results about growth. In particular, I will describe work with Romain Tessera in which we show that if $</td>
<td>A^k</td>
<td>$ is bounded by $Mk^D$ for some given M and D then, provided k is large enough,</td>
<td>A^n</td>
<td>is bounded by $M’n^D$ for <em>every</em> n > k, with M’ depending only on M and D. This verifies a conjecture of Itai Benjamini.</td>
</tr>
</tbody>
</table></div>Matthew Tointontag:www.math.bgu.ac.il,2005:MeetingDecorator/2722017-05-15T17:14:33+03:002017-05-15T17:15:56+03:00<span class="mathjax">Sebastián Donoso: Quantitative multiple recurrence for two and three transformations.</span>May 23, 10:50—12:00, 2017, Math -101<div class="mathjax"><p>In this talk I will provide some counter-examples for quantitative multiple recurrence problems for systems with more than one transformation. For instance, I will show that there exists an ergodic system <span class="kdmath">$(X,\mathcal{X},\mu,T_1,T_2)$</span> with two commuting transformations such that for every <span class="kdmath">$\ell < 4$</span> there exists <span class="kdmath">$A\in \mathcal{X}$</span> such that
<span class="kdmath">$\mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell}$</span>
for every $n \in \mathbb{N}$.
The construction of such a system is based on the study of ``big’’ subsets of <span class="kdmath">$\mathbb{N}^2$</span> and <span class="kdmath">$\mathbb{N}^3$</span> satisfying combinatorial properties.</p>
<p>This a joint work with Wenbo Sun.</p></div>Sebastián Donosohttps://sites.google.com/site/sebastiandonosofuentes/University of O'higginstag:www.math.bgu.ac.il,2005:MeetingDecorator/2452017-03-18T18:05:13+02:002017-04-18T11:39:48+03:00<span class="mathjax">Aryeh Kontorovich: Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path</span>June 13, 10:50—12:00, 2017, Math -101<div class="mathjax"><p>We propose a procedure (the first of its kind) for computing a fully
data-dependent interval that traps the mixing time t_mix of a finite
reversible ergodic Markov chain at a prescribed confidence level. The
interval is computed from a single finite-length sample path from the
Markov chain, and does not require the knowledge of any parameters of
the chain. This stands in contrast to previous approaches, which
either only provide point estimates, or require a reset mechanism, or
additional prior knowledge.</p>
<p>The interval is constructed around the relaxation time t_relax, which
is strongly related to the mixing time, and the width of the interval
converges to zero roughly
at a sqrt{n} rate, where n is the length of the sample path. Upper and
lower bounds are given on the number of samples required to achieve
constant-factor multiplicative accuracy. The lower bounds indicate
that, unless further restrictions are placed on the chain, no
procedure can achieve this accuracy level before seeing each state at
least \Omega(t_relax) times on the average. Finally, future
directions of research are identified.</p>
<p>Join work with Daniel Hsu and Csaba Szepesvári</p></div>Aryeh Kontorovichhttps://www.cs.bgu.ac.il/~karyeh/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2652017-04-19T10:06:32+03:002017-06-15T16:27:37+03:00<span class="mathjax">Amir Yehudayoff: On weak nets</span>June 20, 10:50—12:00, 2017, Math -101<div class="mathjax"><p>We will discuss an equivalence between the existence of weak nets and the Radon number, in an abstractly convex space. Based on work with Shay Moran.</p></div>Amir YehudayoffTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/2702017-05-09T17:33:44+03:002017-06-21T14:48:39+03:00<span class="mathjax">Meng Wu: Furstenbergʼs conjecture on intersections of times 2 and times 3-invariant sets</span>June 27, 10:50—12:00, 2017, Math -101<div class="mathjax"><p>In 1969, H. Furstenberg proposed a conjecture on dimension of intersections of <span class="kdmath">$\times 2$</span> and <span class="kdmath">$\times 3$</span> -invariant sets.
We will present some of the steps involved in a recent solution of this conjecture.</p></div>Meng WuHUJItag:www.math.bgu.ac.il,2005:MeetingDecorator/2812017-06-19T12:47:08+03:002017-06-19T12:47:12+03:00<span class="mathjax">Basheer Abu Khalil: Definition of Chaos In Sense Of Devaney</span>July 12, 11:00—12:00, 2017, Math -101<div class="mathjax"><p>Devaney’s definition of chaos is one of the most popular and widely known. A continuous map f from a compact
metric space (X, d) to itself is chaotic in the sense of Devaney if
(1) f is transitive,
(2) the set of all periodic points of f is dense in X, and
(3) f has sensitive dependence on initial conditions.
we will show that (1) and (2) imply (3) in Devaney’s definition in any metric space. We will show (1) and (3) do not imply (2)
and (2) ; (3) do not imply (1).
We will also show that for continuous maps on an interval in R; transitivity implies that the set of periodic points
is dense. It follows that transitivity implies chaos, and we will give some examples to note that there are no other trivialities in Devaney’s definition when restricted to interval.</p></div>Basheer Abu Khalil