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math.PR2025
Shadow and percolation II: discrete and continuous landscapes with correlations
David Vernotte
In this paper we consider a discrete or continuous landscape with correlations and we consider a source of light (a sun) at infinity emitting parallel rays of light making a slope…
math.PR2025
Shadow and percolation I: discrete landscapes with independence
David Vernotte
Let X be a planar random field on Z^2 which we interpret as a random height function describing some landscape of montains. We consider a source of light (a sun) located at infinit…
math.PR2025
Chemical distance for smooth Gaussian fields in higher dimension
David Vernotte
Gaussian percolation can be seen as the generalization of standard Bernoulli percolation on . Instead of a random discrete configuration on a lattice, we consider a c…