Convergence to equilibrium of biased plane partitions

TL;DR

This paper proves rapid convergence to equilibrium for a biased surface dynamics modeled by plane partitions, establishing spectral gap bounds and mixing times uniform across boundary conditions and system sizes.

Contribution

It introduces a new analysis of biased plane partition dynamics, demonstrating uniform spectral gap bounds and linear mixing times with logarithmic corrections.

Findings

Positive spectral gap uniformly in boundary conditions and system size

Mixing time of order system size M with logarithmic factors

Analysis of non-intersecting path representation of the surface

Abstract

We 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.