

Probability seminar
 Title:
FUNDAMENTAL SOLUTION OF KINETIC FOKKERPLANCK 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 FokkerPlanck 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 BeurlingMalliavin 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.

