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- W4287320094 abstract "We prove upper bounds on the one-arm exponent $eta_1$ for dependent percolation models; while our main interest is level set percolation of smooth Gaussian fields, the arguments apply to other models in the Bernoulli percolation universality class, including Poisson-Voronoi and Poisson-Boolean percolation. More precisely, in dimension $d=2$ we prove $eta_1 le 1/3$ for Gaussian fields with rapid correlation decay (e.g. the Bargmann-Fock field), and in general dimensions we prove $eta_1 le d/3$ for finite-range fields and $eta_1 le d-2$ for fields with rapid correlation decay. Although these results are classical for Bernoulli percolation (indeed they are best-known in general), existing proofs do not extend to dependent percolation models, and we develop a new approach based on exploration and relative entropy arguments. We also establish a new Russo-type inequality for smooth Gaussian fields which we use to prove the sharpness of the phase transition for finite-range fields." @default.
- W4287320094 created "2022-07-25" @default.
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- W4287320094 date "2021-03-01" @default.
- W4287320094 modified "2023-09-27" @default.
- W4287320094 title "Upper bounds on the one-arm exponent for dependent percolation models" @default.
- W4287320094 hasPublicationYear "2021" @default.
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