5 papers
Shadow and percolation III: chemical distance in continuous landscapes with correlations
David Vernotte
We study some geometric properties of the excursion set of a slope field alpha associated to a smooth, planar, centered, Gaussian field f. That, is we consider the set of all point…
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…
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…
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…
Fractal behavior for nodal lines of smooth planar Gaussian fields at criticality
David Vernotte
This paper is devoted to the study of the large scale geometry of the excursion set and nodal set of a planar smooth Gaussian field at criticality . We prove that th…