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Convergence to equilibrium of biased plane Partitions
Author(s) -
Caputo Pietro,
Martinelli Fabio,
Toninelli Fabio Lucio
Publication year - 2011
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20339
Subject(s) - logarithm , partition (number theory) , spectral gap , mathematics , mixing (physics) , monotone polygon , surface (topology) , convergence (economics) , plane (geometry) , boundary (topology) , statistical physics , zero (linguistics) , mathematical analysis , physics , geometry , combinatorics , quantum mechanics , economics , economic growth , linguistics , philosophy
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. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 83–114, 2011