## Probability Seminar: Ohad Feldheim

- Date: 09/25/2013
- Time: 16:00

*Tel Aviv University*

University of British Columbia

Rigidity of 3-colorings of the d-dimensional discrete torus

We prove that a uniformly chosen proper coloring of Z_{2n}^d 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.

Location: ESB 2012