Tel Aviv University
 
Hello everyone,
 
The next colloquium talk will be held on:
 
Monday, 18/3/2012, 12:15, Schreiber 006, Tel Aviv University.
 
Speaker: Dan Romik (University of California, Davis)
 
Title: Random noncrossing matchings arising in percolation theory.
 
The abstract is given below. Tea and coffee at 12:00, same room.
 
Hope to see you there. For information about future colloquia, see
 <http://www.math.tau.ac.il/~ostrover/colloquium/colloq2012.html>
 
Yours,
Yaron
 
*******************************************************
 
Abstract: In probability theory and statistical physics, bond percolation on
the square lattice is a natural model for a porous random medium and
provides one of the simplest examples of a phase transition. At criticality,
it has remarkable long-range correlation properties (many of them still
conjectural). This talk will focus on "connectivity patterns" associated
with a percolation
configuration, which are random noncrossing matchings of the integers that
encode connectivity information. Mysteriously, the probabilities for
interesting events on connectivity patterns are dyadic rational numbers such
as 3/8, 59/1024 and 69693/2^21. This "rationality phenomenon" can be proved
in a few cases but remains mostly conjectural. I will describe the
background and history of the model as well as new results that shed light
on the problem by reducing the
proof of the rationality phenomenon to a family of purely algebraic
identities about coefficients of certain multivariate polynomials.
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from:  <ostrover@post.tau.ac.il>