Roman Kotecký

Mathematics Institute, University of Warwick


"Emergence of large cycles for random interchanges on a hypercube"

Phase transitions for quantum spin lattice models can be shown to be linked with the existence of large cycles for random interchanges of sites of the corresponding lattice. While for complete graphs the random interchanges are well understood (cards shuffling), the emergence of large cycles for lattices is an entirely open problem. The case of hypercube is a first step in this direction. Based on a joint paper with P. Milos and D. Ueltschi.