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- W4311430090 abstract "In a recent work (arXiv:2206.10724), Muirhead has studied level-set percolation of (discrete or continuous) Gaussian fields, and has shown sharpness of the associated phase transition under the assumption that the field has a certain multiscale white noise decomposition, a variant of a finite-range decomposition. We show that a large class of Gaussian field have such a white noise decomposition with optimal decay parameter. Examples include the discrete Gaussian free field, the discrete membrane model, and the mollified continuous Gaussian free field. This answers various questions from Muirhead's paper. Our construction of the white-noise decomposition is a refinement of Bauerschmidt's construction of finite-range decomposition. In the continuous setting our construction is very similar to Bauerschmidt's, while in the discrete setting several new ideas are needed, including the use of a result by P'olya and SzegH{o} on polynomials that take positive values on the positive real line." @default.
- W4311430090 created "2022-12-26" @default.
- W4311430090 creator A5088453187 @default.
- W4311430090 date "2022-12-12" @default.
- W4311430090 modified "2023-09-24" @default.
- W4311430090 title "Finite range decompositions of Gaussian fields with applications to level-set percolation" @default.
- W4311430090 doi "https://doi.org/10.48550/arxiv.2212.05756" @default.
- W4311430090 hasPublicationYear "2022" @default.
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