Alexis Prévost

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math.PR2024

First passage percolation, local uniqueness for interlacements and capacity of random walk

Alexis PrÃ©vost

The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $Z^{d}$ , $d \geq 3$ , the FP…

math.PR2024

Percolation for two-dimensional excursion clouds and the discrete Gaussian free field

Alexander Drewitz, Olof Elias, Alexis PrÃ©vost +2

We study percolative properties of excursion processes and the discrete Gaussian free field (dGFF) in the planar unit disk. We consider discrete excursion clouds, defined using ran…

math.PR2024

Geometry of Gaussian free field sign clusters and random interlacements

For a large class of amenable transient weighted graphs $G$ , we prove that the sign clusters of the Gaussian free field on $G$ fall into a regime of strong supercriticality, in whi…