Convergence to equilibrium of biased plane Partitions

Abstract

AbstractWe study a single‐flip dynamics for the monotone surface in (2 + 1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non‐intersecting simple paths. When the flips have a non‐zero bias we prove that there is a positive spectral gap uniformly in the boundary conditions and in the size of the system. Under the same assumptions, for a system of size M, the mixing time is shown to be of order M up to logarithmic corrections. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 83–114, 2011