Hyperspaces infection12/25/2023 ![]() The proofs use stochastic approximation algorithms. What is the limiting behavior of the proportion of balls in the bins? We will present results for alpha ≤ 1. At discrete times, a ball is added to each pair of bins as follows: one of the bins gets the ball with probability proportional to its current number of balls raised by some fixed power alpha > 0. Given a finite connected graph, place a bin at each vertex, and call two bins a pair if they share an edge. The second is a Polya's urn with graph based interactions. What is the limiting distribution at the root node, as the height of the tree grows? We will present results for some instances of this problem. Given an infection configuration in the leaves, and given a set of spreading rules, the infection spreads along the nodes of the tree. The first one considers annihilation and coalescence on finite binary trees. SOME PROBABILISTIC RESULTS USING DYNAMICSWhen: Thu, Septem2:00pmĪbstract: We will discuss two problems that are probabilistic in nature and are solved using dynamics. Our examples will be via the method of cutting and stacking. We will also construct examples of transformations that have these desired properties. ![]() During this talk we will discuss rigid verses various types of weakly mixing in infinite ergodic theory. Speaker: Kelly Yancey- University of Maryland- In the setting of infinite ergodic theory, measure-preserving transformations that are rigid and spectrally weakly mixing are generic in the sense of Barie category. Rigid and weak mixing constructions preserving an infinite measureWhen: Thu, Septem2:00pm This is joint work with Kathryn Lindsey from Cornell University. I will end with some open questions about the structure of this space and relevant questions about dimension groups. I will state a criterion for unique ergodicity for adic transformations, explain where it comes from, and talk a bit about the space of all Bratteli diagrams, which in some sense serves as a moduli space for all flat surfaces of finite area, and the systems which they model. Using recently-developed tools for the study of translation flows on flat surfaces of infinite type, we can study the ergodic properties through the flat surface model in very general terms. In fact, using Rolkhlin's lemma, one can do this construction for any aperiodic automorphism of a standard measure space. Using Rokhlin towers one can construct a flat surface (generically of infinite topological type) and a flow on it which is measurably isomorphic to the dynamics of the Bratteli-Vershik (adic) transformation. It is defined by an infinite directed graph called a Bratteli diagram with some lexicographic order on the set of infinite paths through this graph. Speaker: Rodrigo Trevino- Tel Aviv UniversityĪbstract: A Bratteli-Vershik transformation, also known as an adic transformation, is a measure preserving transformation of a zero dimensional set. ![]() Dynamics Archives for Fall 2013 to Spring 2014įlat surface models of ergodic systemsWhen: Thu, Septem2:00pm ![]()
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