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- W1569604497 abstract "We continue our study of large deviations of the empirical measures of a massless Gaussian field on $mathbb Z^d$, whose covariance is given by the Green function of a long-range random walk. In this paper we extend techniques and results of Bolthausen and Deuschel to the nonlocal case of a random walk in the domain of attraction of the symmetric $alpha$-stable law, with $alpha in (0, 2 wedge d)$. In particular, we show that critical large deviations occur at the capacity scale $N^{d-alpha}$, with a rate function given by the Dirichlet form of the embedded $alpha$-stable process. We also prove that if we impose zero boundary conditions, the rate function is given by the Dirichlet form of the killed $alpha$- stable process." @default.
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- W1569604497 date "2001-02-01" @default.
- W1569604497 modified "2023-09-25" @default.
- W1569604497 title "Critical large deviations in harmonic crystals with long-range interactions" @default.
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- W1569604497 doi "https://doi.org/10.1214/aop/1008956329" @default.
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