David Vernotte

activity

20232026

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6 papers · 1 filter

math.PR2026

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…

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 $Z^{d}$ . Instead of a random discrete configuration on a lattice, we consider a c…

math.PR2024

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 $ℓ = ℓ_{c} = 0$ . We prove that th…

math.PR2023

Chemical distance in the supercritical phase of planar Gaussian fields

David Vernotte

Our study concerns the large scale geometry of the excursion set of planar random fields: E $ℓ$ = {x $\in$ R 2 |f (x) $\geq$ - $ℓ$ }, where $ℓ$ $\in$ R is a real paramet…