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Gaussian Free Field in an Interlacing Particle System with Two Jump Rates
Author(s) -
Duits Maurice
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21419
Subject(s) - interlacing , gaussian free field , jump , mathematics , gaussian , statistical physics , limit (mathematics) , particle system , lattice (music) , mathematical analysis , physics , quantum mechanics , computer science , acoustics , operating system
We study the fluctuations of a random surface in a stochastic growth model on a system of interlacing particles placed on a two‐dimensional lattice. There are two different types of particles, one with a low jump rate and the other with a high jump rate. In the large time limit, the random surface has a deterministic shape. Due to the different jump rates, the limit shape and the domain on which it is defined are not smooth. The main result is that the fluctuations of the random surface are governed by the Gaussian free field. © 2012 Wiley Periodicals, Inc.