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


September 20, 2013


Naomi Feldheim and Ohad Feldheim


Tel Aviv University


SPEAKER: Naomi Feldheim
TITLE: Gap probabilities for zeroes of stationary Gaussian functions
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).

SPEAKER: Ohad Feldheim
TITLE: Rigidity of 3-colorings of the d-dimensional discrete torus
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.


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 :

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