Combinatorics: Yinon Spinka (TAU) "Long-range order in random colorings and random graph homomorphisms in high dimensions"

Speaker: Yinon Spinka (TAU)
Title: Long-range order in random colorings and random graph homomorphisms in high dimensions
Abstract:
Consider a uniformly chosen proper coloring with q colors of a domain in Z^d (a graph homomorphism to a clique). We show that when the dimension is much higher than the number of colors, the model admits a staggered long-range order, in which one bipartite class of the domain is predominantly colored by half of the q colors and the other bipartite class by the other half. The q=3 case was previously known. The result further extends to homomorphisms to other graphs, allowing also vertex and edge weights (positive temperature models). The results apply also in low dimensions d>=2 if one works with a sufficiently `thickened' version of Z^d. Joint work with Ron Peled.

Date: 

Mon, 16/01/2017 - 11:00 to 13:00

Location: 

Rothberg B220 (CS bldg)