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Annales de l’Institut Henri Poincaré D

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Volume 6, Issue 4, 2019, pp. 489–532
DOI: 10.4171/AIHPD/77

Published online: 2019-09-04

Speed and fluctuations for some driven dimer models

Sunil Chhita[1], Patrik L. Ferrari[2] and Fabio L. Toninelli[3]

(1) Durham University, UK
(2) Universität Bonn, Germany
(3) Université Lyon 1, Villeurbanne, France

We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth model of an interface, belonging to the anisotropic KPZ universality class. We use a combinatorial approach to determine the speed of growth and show logarithmic growth in time of the variance of the height function.

Keywords: Random surfaces, interacting particle systems, random tilings, limit shapes, determinantal processes, Kasteleyn matrices

Chhita Sunil, Ferrari Patrik, Toninelli Fabio: Speed and fluctuations for some driven dimer models. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 489-532. doi: 10.4171/AIHPD/77