Probability seminar
 
 
 
 
  • Title: OIL AND WATER
  • Speaker: Christopher Hoffman (University of Washington)
  • Time: 2:30 p.m., Monday, October 20, 2014
  • Room: LOW 117
  • Abstract: We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with $n$ ``oil'' and $n$ ``water'' particles at the origin, the particles diffuse in $\bf Z$ according to the following rule: whenever some site $x \in\bf Z$ has at least 1 oil and at least 1 water particle present, it fires by sending 1 oil particle and 1 water particle each to an independent random neighbor $x \pm 1$. Firing continues until every site has at most one type of particles. We establish the correct order for several statistics of this model and identify the scaling limit under assumption of existence.

    This is joint work with Elisabetta Candellero, Shirshendu Ganguly and Lionel Levine.


 
 
  • Title: FUNDAMENTAL SOLUTION OF KINETIC FOKKER-PLANCK OPERATOR WITH ANISOTROPIC NONLOCAL DISSIPATIVITY
  • Speaker: Xicheng Zhang (Wuhan University, China)
  • Time: 2:30 p.m., Monday, October 13, 2014
  • Room: LOW 117
  • Abstract: By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic Levy process, and the drift term is allowed to be cubic growth.

 
 
  • Title: DETERMINANTAL PROBABILITY: SURPRISING RELATIONS
  • Speaker: Russell Lyons (Indiana University)
  • Time: 2:30 p.m., Monday, October 6, 2014
  • Room: LOW 117
  • Abstract: (1) For each subset $A$ of the circle with measure $m$, there is a sequence of integers of Beurling-Malliavin density $m$ such that the set of corresponding complex exponentials is complete for $L^2(A)$. (2) Given an infinite graph, simple random walk on each tree in the wired uniform spanning forest is a.s. recurrent. (3) Let $Z$ be the set of zeroes of a random Gaussian power series in the unit disk. Then a.s., the only function in the Bergman space that vanishes on $Z$ is the zero function. (4) In our talk, we explain a theorem that has (1) and (2) as corollaries. We also describe a conjectural extension that has (3) (which is not known) as a corollary. All these depend on determinantal probability measures. All terms above will be explained.

 
 
  • Title: A GAS PARTICLE IN A GRAVITATIONAL FIELD
  • Speaker: Douglas Rizzolo (Univeristy of Washington)
  • Time: 2:30 p.m., Monday, September 29, 2014
  • Room: LOW 117
  • Abstract: We will discuss the motion a tagged gas particle in a gravitational field. Our starting point will be a Markov approximation to a Lorentz gas model with variable density. We investigate how the density of the ambient gas impacts the recurrence or transience of the tagged particle. Additionally, we will show that there are multiple scaling regimens leading to nontrivial diffusive limits. This talk is based on joint work with Krzysztof Burdzy.

 
 

 
 
Last modified: October 14, 2014, 16:10        Bookmark and Share