Publication: Entropic repulsion for a class of Gaussian interface models in high dimensions
Entropic repulsion for a class of Gaussian interface models in high dimensions
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Kurt, N. (2007). Entropic repulsion for a class of Gaussian interface models in high dimensions. Stochastic Processes and Their Applications, 117(1), 23–34. https://doi.org/10.1016/j.spa.2006.05.011
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Consider the centred Gaussian field on the lattice View the MathML source, d large enough, with covariances given by the inverse of View the MathML source, where Δ is the discrete Laplacian and View the MathML source, 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 k
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- Kurt, N
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Kurt, N. (2007). Entropic repulsion for a class of Gaussian interface models in high dimensions. Stochastic Processes and Their Applications, 117(1), 23–34. https://doi.org/10.1016/j.spa.2006.05.011
