Gap Probabilities for Zeroes of Stationary Gaussian Functions & Rigidity of 3-Colorings of the d-Dimensional Discrete Torus

Date

September 20, 2013

Speaker

Naomi Feldheim and Ohad Feldheim

Affiliation

Tel Aviv University

Overview

TALK 1:
SPEAKER: Naomi Feldheim
TITLE: Gap probabilities for zeroes of stationary Gaussian functions
ABSTRACT:
We consider real stationary Gaussian functions on the real axis
and discuss the “gap probability” (i.e., the probability
that the function has no zeroes in [0,T]). We give sufficient conditions
for this probability to be roughly exponential in T.
(Joint work with Ohad Feldheim).

TALK 2:
SPEAKER: Ohad Feldheim
TITLE: Rigidity of 3-colorings of the d-dimensional discrete torus
ABSTRACT:
We prove that a uniformly chosen proper coloring of Z2nd with 3 colors has a very rigid structure when the dimension d is sufficiently high. The coloring almost surely takes one color on almost all of either the even or the odd sub-lattice. In particular, one color appears on nearly half of the lattice sites. This model is the zero temperature case of the 3-states anti-ferromagnetic Potts model, which has been studied extensively in statistical mechanics. The proof involves results about graph homomorphisms and various combinatorial methods, and follows a topological intuition. Joint work with Ron Peled.

Speakers

Naomi Feldheim and Ohad Feldheim

Naomi Feldheim is a PhD student at Tel Aviv University, specializing in Gaussian random functions. Her advisor is Michael Sodin. See : http://www.tau.ac.il/~friedeln/index.html

Ohad Feldheim just finished his PhD under the direction of Noga Alon at Tel Aviv University, and is currently a postdoc at the Weizmann Institute. His research is on the interface of Combinatorics, discrete geometry and probability. See http://www.tau.ac.il/~ohadfeld/index.html

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