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- W4287183791 abstract "We study random surfaces with a uniformly convex gradient interaction in the presence of quenched disorder taking the form of a random independent external field. Previous work on the model has focused on proving existence and uniqueness of infinite-volume gradient Gibbs measures with a given tilt and on studying the fluctuations of the surface and its discrete gradient. In this work we focus on the convergence of the thermodynamic limit, establishing convergence of the finite-volume distributions with Dirichlet boundary conditions to translation-covariant (gradient) Gibbs measures. Specifically, it is shown that, when the law of the random field has finite second moment and is symmetric, the distribution of the gradient of the surface converges in dimensions $dgeq4$ while the distribution of the surface itself converges in dimensions $dgeq 5$. Moreover, a power-law upper bound on the rate of convergence in Wasserstein distance is obtained. The results partially answer a question discussed by Cotar and Kulske" @default.
- W4287183791 created "2022-07-25" @default.
- W4287183791 creator A5089811297 @default.
- W4287183791 date "2021-05-09" @default.
- W4287183791 modified "2023-09-25" @default.
- W4287183791 title "Convergence to the thermodynamic limit for random-field random surfaces" @default.
- W4287183791 doi "https://doi.org/10.48550/arxiv.2105.03940" @default.
- W4287183791 hasPublicationYear "2021" @default.
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