arXiv subjects

Aurelia Deshayes

Publications and source records attributed to Aurelia Deshayes.

7 recordsLinked to original sources

arXiv2026

The Contact Process Can Survive on a Slightly Subcritical Dynamical Percolation Cluster

The contact process on dynamic edges (CPDE) is a contact process evolving on a dynamic environment given by a dynamical percolation on the edges of Z d\,: each edge updates its state to open or closed with respective rates vp and v(1 -p). By coupling a well-chosen subset of once infected sites in the CPDE with a cluster of some supercritical percolation on the edges of Z d , we prove that, for every dimension d $\ge$ 2, we can find some slightly subcritical p < pc(d) such that for every update speed v > 0, the contact process with large enough infection rate can survive. This extends the result for dimension 1 proved by Linker and Remenik in [LR20].

math.PR↗

arXiv2026

Finding the convex envelope of a boundary datum using random geometric graphs

In this paper we approximate the convex envelope of a boundary datum inside a bounded domain in the Euclidean space. We work with a random graph that is obtained as random points with uniform distribution that are connected by proximity ($x\sim y$ when $|x-y|<r$). On the graph we solve an equation (that approximate the first eigenvalue of the Hessian of a smooth function) with an exterior datum. Under appropriate assumptions on $r$ we show that the unique solution to the equation in the graph converges to the convex envelope of the boundary datum as the number of points goes to infinity.

math.AP↗

arXiv2025

An asymptotic shape theorem for additive random linear growth models

In this paper, we define a class of additive random growth models whose growth is at least and at most linear and prove an asymptotic shape theorem for these models. This proof generalizes already known proofs for the classical contact process or some of its variants and allows us to obtain conjectured asymptotic shape theorems for Richardson's model with stirring and the contact process with stirring.

math.PR↗

arXiv2025

The Rightmost Particle of the Contact Process on Dynamic Random Environments

We study the behaviour of the rightmost occupied site in two models: the Spont process and the contact process with inherited sterility, in dimension 1. Both can be viewed as contact processes evolving in dynamic random environments, where the environment may itself depend on the state of the process. In the Spont process, blocking particles appear spontaneously, while in the inherited sterility model, sterile sites arise as offspring of occupied ones. Each model presents distinct mathematical challenges: the Spont process lacks self-duality, whereas the inherited sterility process is non-attractive. We establish a law of large numbers and a central limit theorem for the position of the rightmost occupied site. Our approach is based on the construction of a sequence of renewal times, defined through a detailed analysis of active infection paths. These results are obtained in the supercritical regime of the Spont process.

math.PR↗

arXiv2018

Front evolution of the Fredrickson-Andersen one spin facilitated model

The Fredrickson-Andersen one spin facilitated model (FA-1f) on Z belongs to the class of kinetically constrained spin models (KCM). Each site refreshes with rate one its occupation variable to empty (respectively occupied) with probability q (respectively $p = 1 - q$), provided at least one nearest neighbor is empty. Here, we study the non equilibrium dynamics of FA-1f started from a configuration entirely occupied on the left half-line and focus on the evolution of the front, namely the position of the leftmost zero. We prove, for q larger than a threshold $\bar{q} < 1$, a law of large numbers and a central limit theorem for the front, as well as the convergence to an invariant measure of the law of the process seen from the front.

math.PR↗

arXiv2018

Scaling limit of subcritical contact process

In this paper we describe the subcritical contact process on $\Z^d$ for large times, starting with all sites infected. The configuration is described in terms of the macroscopic locations of infected regions in space and the relative positions of infected sites in each such region.

math.PR↗

arXiv2014

The contact process with aging

In this article, we introduce a contact process with aging: in this generalization of the classical contact process, each particle has an integer age that influences its ability to give birth. We prove here a shape theorem for this process conditioned to survive. In order to establish some key exponential decays, we adapt the Bezuidenhout and Grimmett construction [BG91] to build a coupling between our process and a supercritical oriented percolation. Our results also apply to the two-stage contact process introduced by Krone [Kro92].

math.PR↗