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Stochastic dynamics of discrete interfaces and dimer models

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We will study some effective models, called dimer models, for the interface between two coexisting thermodynamical phases in three dimension. We will show in a relatively general setup that the time needed for the system to reach equilibrium is of order L^(2+o(1)), where L is the typical length scale of the system. The exponent 2 is optimal. More precisely, for surfaces attached to a curve drawn in some plane, we will control the mixing time for several models, including lozenge tilings and domino tilings. For surfaces attached to a general curve, we will only work with lozenges and use a weaker notion of “macroscopic” convergence.

This talk is part of the Probability series.

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