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: Oren Louidor, University of California, Los Angeles
Title: Isoperimetry in Supercritical Percolation
 
Date: Monday, December 17
Time: 14:30
Place: Schreiber 309
 
Abstract:
We consider the unique infinite connected component of supercritical
bond percolation on the square lattice and study the geometric
properties of isoperimetric sets, i.e., sets with minimal boundary
for a given volume. For almost every realization of the infinite
connected component we prove that, as the volume of the isoperimetric
set tends to infinity, its asymptotic shape can be characterized by
an isoperimetric problem in the plane with respect to a particular
norm. As an application we then show that the anchored isoperimetric
profile with respect to a given point as well as the Cheeger constant
of the giant component in finite boxes scale to deterministic
quantities. This settles a conjecture of Itai Benjamini for the
plane. Joint work with M. Biskup, E. Procaccia and R. Rosenthal.
 
Best regards,
   Ron
 
Seminar webpage:
 <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Peled   <peledron@post.tau.ac.il>