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

Speaker  Naomi Feldheim and Ohad Feldheim

Affiliation  Tel Aviv University

Host  Yuval Peres

Duration  01:20:02

Date recorded  20 September 2013

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.

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