While classical “integrable” statistical mechanics has been restricted to one and two dimensions, recent ideas have extended our understanding to (some) higher dimensional situations, or to models on non-planar graphs. These include graph limits, posets, multinomial models, random complexes and random groups, and more. While these topics are quite diverse, they nonetheless have common tools, notably the use of random walks, the graph laplacian, homology theory, and determinants. Topics will include: Benjamini-Schramm limits of graphs, unimodular measures, spanning trees and spanning complexes, chip firing/sandpile models, matroids, higher determinantal processes, random complexes, multinomial models, random groups, rigidity, and statistical physics in more than two dimensions.
(California Institute of Technology)
Richard Kenyon (Yale University)
Gady Kozma (Weizmann Institute of Science)
Asaf Nachmias (Tel Aviv University)
Perla Sousi (University of Cambridge)