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- W4288346064 abstract "Let f be a stationary isotropic non-degenerate Gaussian field on R^2. Assume that f = q * W where q is both C^2 and L^2 and W is the L^2 white noise on R^2. We extend a result by Stephen Muirhead and Hugo Vanneuville by showing that, assuming that q * q is pointwise non-negative and has fast enough decay, the set {f > -l} percolates with probability one when l > 0 and with probability zero if l < 0 or l = 0. We also prove exponential decay of crossing probabilities and uniqueness of the unbounded cluster. To this end, we study a Gaussian field g defined on the torus and establish a superconcentration formula for the threshold T(g) which is the minimal value such that {g > -T(g)} contains a non-contractible loop. This formula follows from a Gaussian Talagrand type inequality." @default.
- W4288346064 created "2022-07-29" @default.
- W4288346064 creator A5049983992 @default.
- W4288346064 date "2019-05-30" @default.
- W4288346064 modified "2023-10-14" @default.
- W4288346064 title "Talagrand's inequality in planar Gaussian field percolation" @default.
- W4288346064 doi "https://doi.org/10.48550/arxiv.1905.13317" @default.
- W4288346064 hasPublicationYear "2019" @default.
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