Probability seminar
 Title: A SPATIAL GENERALIZATION OF KINGMAN'S COALESCENT Speaker: Dan Lanoue (University of California, Berkeley) Time: 2:30 p.m., Monday, November 3, 2014 Room: LOW 117 Abstract: The Metric Coalescent (MC) is a measure-valued Markov Process generalizing the classical Kingman Coalescent. We show how the MC arises naturally from a discrete agent based model (the Compulsive Gambler process) of social dynamics and prove an existence and uniqueness theorem extending the MC to the space of all Borel probability measures on any locally compact Polish space. We'll also look in depth at the case of the MC on the unit interval.     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.