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Invariance principle for a solid-on-solid interface model

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Abstract

A stochastic process describing the behavior of the solid-on-solid interface in a strip of widthL is studied. The invariant and reversible measure for the process is the Gibbs state with HamiltonianHΣ|η(x)−η(x+1)|. Under “free” boundary conditions, we show that the height of the moving interface at any site converges, when suitable renormalized, to Brownian motion with a diffusion coefficient proportional toL −1.

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Authors and Affiliations

  1. Instituto de Matemática e Estatistica, Universidade de São Paulo, 05508, São Paulo, Brazil

    Pablo A. Ferrari

  2. Institute for Theoretical Physics, University of California, 93106, Santa Barbara, California

    Pablo A. Ferrari

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  1. Pablo A. Ferrari
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Ferrari, P.A. Invariance principle for a solid-on-solid interface model. J Stat Phys 51, 1077–1090 (1988). https://doi.org/10.1007/BF01014900

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