The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
A loop configuration on the hexagonal (honeycomb) lattice is a finite subgraph of the lattice in which every vertex has degree 0 or 2, so that every connected component is isomorphic to a cycle. The loop O(n) model on the hexagonal lattice is a random loop configuration, where the probability of a loop configuration is proportional to x^(#edges) n^(#loops) and x,n>0 are parameters called the edge-weight and loop-weight. We show that for sufficiently large n, the probability that the origin is surrounded by a loop of length k decays exponentially in k. In this same region of parameters, we also show a phase transition from a disordered phase to an ordered phase.
Joint work with Hugo Duminil-Copin, Ron Peled and Wojciech Samotij.
Biography:
Yinon completed his undergraduate studies in mathematics and physics and his MSc in pure mathematics at Tel-Aviv University. Today Yinon is a PhD student at Tel-Aviv University, where he researches problems in the interface between probability theory and mathematical physics. His research concentrates on models from statistical mechanics, such as the Potts model and the O(n) model, and is directed primarily towards understanding the physical phenomenon of phase transition in models with hard constraints.