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The paper concerns lattice triangulations, i.e., triangulations of the integer points in a polygon in R<sup>2</sup> whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects in their own right and by virtue of applications in algebraic geometry. Our focus is on random triangulations in which a… (More)

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… (More)

We consider random lattice triangulations of n×k rectangular regions with weight λ |σ| where λ > 0 is a parameter and |σ| denotes the total edge length of the triangulation. When λ ∈ (0, 1) and k is fixed, we prove a tight upper bound of order n 2 for the mixing time of the edge-flip Glauber dynamics. Combined with the previously known lower bound of order… (More)

We consider spin systems on the integer lattice graph Z d with nearest-neighbor interactions. We develop a combinatorial framework for establishing that exponential decay with distance of spin correlations, specifically the strong spatial mixing condition (SSM), implies rapid mixing of a large class of Markov chains. As a first application of our method we… (More)

We analyze the mixing time of a natural local Markov Chain (Gibbs sampler) for two commonly studied models of random surfaces: (i) discrete monotone surfaces in Z 3 with almost planar boundary conditions and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model. In both cases we prove the first almost optimal bounds O(L 2 polylog(L)) where L is the… (More)

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