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Entropic repulsion for a class of Gaussian interface models in high dimensions

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  • Kurt, Noemi

Abstract

Consider the centred Gaussian field on the lattice , d large enough, with covariances given by the inverse of , where [Delta] is the discrete Laplacian and , the qj satisfying certain additional conditions. We extend a previously known result to show that the probability that all spins are nonnegative on a box of side-length N has an exponential decay at a rate of order Nd-2klogN. The constant is given in terms of a higher-order capacity of the unit cube, analogously to the known case of the lattice free field. This result then allows us to show that, if we condition the field to stay positive in the N-box, the local sample mean of the field is pushed to a height of order .

Suggested Citation

  • Kurt, Noemi, 2007. "Entropic repulsion for a class of Gaussian interface models in high dimensions," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 23-34, January.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:1:p:23-34
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    Cited by:

    1. Cipriani, Alessandra & Hazra, Rajat Subhra, 2015. "Thick points for a Gaussian Free Field in 4 dimensions," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2383-2404.
    2. Chen, Joe P. & Ugurcan, Baris Evren, 2015. "Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4632-4673.
    3. Cipriani, Alessandra & Hazra, Rajat Subhra & Ruszel, Wioletta M., 2018. "The divisible sandpile with heavy-tailed variables," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3054-3081.

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