Publications de Daniel Rodrigues Valesin

The asymmetric multitype contact process

Thomas Mountford, Daniel Rodrigues Valesin

We study the multitype contact process on Z(d) under the assumption that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, ...

ELSEVIER SCIENCE BV2019

Equilibrium of the interface of the grass-bushes-trees process

Thomas Mountford, Daniel Rodrigues Valesin

2018

Exponential extinction time of the contact process on finite graphs

Thomas Mountford, Daniel Rodrigues Valesin, Jean-Christophe Mourrat

We study the extinction time tau of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degr ...

Elsevier Science Bv2016

Functional Central Limit Theorem for the Interface of the Symmetric Multitype Contact Process

Thomas Mountford, Daniel Rodrigues Valesin

We study the interface of the symmetric multitype contact process on Z. In this process, each site of Z is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give birth with rate 2R lambda; the ...

Impa2016

Metastable densities for the contact process on power law random graphs

Thomas Mountford, Daniel Rodrigues Valesin

We consider the contact process on a random graph with a fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett [2], who showed that for arbitrarily small infection parameter lambda, the survival time of the process is ...

Univ Washington, Dept Mathematics2013

Supercriticality of an annealed approximation of Boolean networks

Thomas Mountford, Daniel Rodrigues Valesin

We consider a model recently proposed by Chatterjee and Durrett [1] as an "annealed approximation" of boolean networks, which are a class of cellular automata on a random graph, as defined by S. Kauffman [5]. The starting point is a random directed graph o ...

Univ Washington, Dept Mathematics2013

The Contact Process : Competition Models and Boolean Networks

Daniel Rodrigues Valesin

This work is a study of three interacting particle systems that are modified versions of the contact process. The contact process is a spin system defined on a graph and is commonly taken as a model for the spread of an infection in a population; transmiss ...

EPFL2011

Multitype Contact Process on Z: Extinction and Interface

Daniel Rodrigues Valesin

We consider a two-type contact process on Z in which both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is confined to a finite ...

2010

Tightness for the interface of the one-dimensional contact process

Thomas Mountford, Daniel Rodrigues Valesin

We consider a symmetric, finite-range contact process with two types of infection; both have the same (supercritical) infection rate and heal at rate 1, but sites infected by Infection I are immune to Infection 2. We take the initial configuration where si ...

2010