Tel Aviv University 
 
Dear all,
 
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
 
Speaker: Asaf Nachmias, University of British Columbia
Title: Random walks on planar graphs via circle packings
 
Date: Monday, May 13
Time: 14:30
Place: Schreiber 309
 
Abstract:
I will describe two results concerning random walks on planar graphs
and the connections with Koebe's circle packing theorem (which I will
not assume any knowledge of):
1. A bounded degree planar triangulation is recurrent if an only if
the set of accumulation points of its circle packing is a polar set
(that is, has zero logarithmic capacity). This extends a result of He
and Schramm who proved recurrence (transience) when the set of
accumulation points is empty (a closed Jordan curve). Joint work with
Ori Gurel-Gurevich and Juan Souto.
2. The Poisson boundary (the space of bounded harmonic functions) of a
transient bounded degree triangulation of the plane is characterized
by the topological boundary obtained by circle packing the graph in
the unit disk. In other words, any bounded harmonic function on the
graph is the harmonic extension of some measurable function on the
boundary of the unit disc. Joint work with Omer Angel, Martin Barlow
and Ori Gurel-Gurevich.
 
Best regards,
   Ron
Seminar webpage:
 <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html>
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Peled   <peledron@post.tau.ac.il>