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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.
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Sunil Chhita, Patrik L. Ferrari, Fabio L. Toninelli, Speed and fluctuations for some driven dimer models. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 4, pp. 489–532DOI 10.4171/AIHPD/77