ANALYSIS
SEMINAR

"Harmonic Functions
and Large Deviations for Random Walk in a Random Environment"

by

Atilla Yılmaz

(Boğaziçi University)

Abstract: Consider random walk in any finite dimension. It
has a typical average velocity. Conditioning it to have some other velocity corresponds
to tilting its transition kernel with some exponential term. This is formalized
in the framework of the theory of large deviations which deals
with exponential rates of
decay of probabilities of rare events. The same connection holds also in the context
of random walk in a random environment (RWRE), except that it is not enough to
just tilt the (now random) transition kernel by a deterministic exponential
term. One has to perform an additional change of measure involving a harmonic
function for the tilted transition kernel. This talk will not assume any prior
knowledge of large deviations or RWRE.

Tea and cookies will be served before the
seminar.

Date:
Thursday, May  10, 2012

Time: 15.40 – 16:30

Place: Mathematics Seminar Room,
SA-141