Convergence to equilibrium of biased plane partitions

Details Convergence to equilibrium of biased plane partitions Convergence to equilibrium of biased plane partitions

2009-03-29

arxiv.org/abs/0903.5079v3

Mathematics

Probability

32 pages, 9 figures; v2 minor revision; to be published in Random Structures & Algorithms

Scientific paper

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.

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