Tel Aviv University
Hello everyone,
The next colloquium talk will be held on:
Monday, 14/01/2013, 12:15, Schreiber 006, Tel Aviv University.
Speaker: Ofer Zeitouni (Weizmann Institute)
Title: From KPP equations to the maxima of Gaussian free fields
The abstract is given below. Tea and coffee at 12:00, same room.
Hope to see you there. For information about future colloquia, see
Abstract: The Fisher-Kolmogorov-Petrovsky-Piscounov equation describes the
propagation of a self interacting wave such as in flame propagation.
Probabilistically, for appropriate initial conditions it describes the
evolution of the location of the maximal particle in a system of branching
random walks (where the total population size increases exponentially). That
particle system was analyzed by Bramson using a mixture of probabilistic and
analytic methods in the early 80's. In particular, the ``front'' of the
propagating wave is delayed (by a logarithmic factor) behind the
stationary, linear speed propagation.
The Gaussian free field is a random Gaussian field that is indexed by points
in $R^d$; in the critical dimension d=2, it represents a random
A discrete analogue of the GFF can be defined on any finite graph. Of
interest are properties of the maxima of the field, and in particular the
fluctuations of the maximum.
After describing a general point of view  that allows one to analyze
branching particle systems, I will describe newly observed  phase
transitions that occur in the case of time-inhomogeneous media. I will then
describe recent work
that links the two objects, branching random walks and Gaussian free fields,
in the critical dimension $d=2$. In particular, I will explain how Bramson's
work can be adapted in order to show that the maximum of the two
dimensional (discrete) GFF has fluctuations which are of order $1$. The talk
is based on joint works with Maury Bramson, with Jian Ding and with Ming
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from:  <ostrover@post.tau.ac.il>