- Series
- Combinatorics Seminar
- Time
- Friday, March 29, 2019 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Yinon Spinka – University of British Columbia, Vancouver, Canada
- Organizer
- Prasad Tetali
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. In the q=3 case, this was previously shown by Galvin-Kahn-Randall-Sorkin and independently by Peled. The result further extends to homomorphisms to other graphs (covering for instance the cases of the hard-core model and the Widom-Rowlinson model), allowing also vertex and edge weights (positive temperature models). Joint work with Ron Peled.