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

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

Supercriticality conditions for asymmetric zero-range process with sitewise disorder

Thomas Mountford

We discuss necessary and sufficient conditions for the convergence of disordered asymmetric zero-range process to the critical invariant measure. ...

Brazilian Statistical Association2015

Feynman-Kac representation for the parabolic Anderson model driven by fractional noise

Thomas Mountford, Kamran Kalbasi

We consider the parabolic Anderson model driven by fractional noise: partial derivative/partial derivative t u(t,x) = k Delta u(t,x) + u(t,x)partial derivative/partial derivative t W(t,x) x is an element of Z(d), t >= 0, where k > 0 is a diffusion constant ...

Academic Press Inc Elsevier Science2015

Lyapunov exponents of random walks in small random potential: the upper bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on Z(d) evolving in a random i.i.d. potential taking values in [0, +infinity). The potential is not assumed integrable, and can be rescaled by a multiplicative factor lambda > 0. Completing the work started in a companion ...

Univ Washington, Dept Mathematics2015

Random walks generated by equilibrium contact processes

Thomas Mountford

We consider dynamic random walks where the nearest neighbour jump rates are determined by an underlying supercritical contact process in equilibrium. This has previously been studied by den Hollander and dos Santos (arXiv: 1209.1511). We show the CLT for s ...

Univ Washington, Dept Mathematics2015

Ergodic behaviour of "signed voter models"

Thomas Mountford, Grégory Maillard

We answer some questions raised by Gantert, Lowe and Steif (Ann. Inst. Henri Poincare Probab. Stat. 41 (2005) 767 780) concerning "signed" voter models on locally finite graphs. These are voter model like processes with the difference that the edges are co ...

Inst Mathematical Statistics2013

Lyapunov Exponents of Random Walks in Small Random Potential: The Lower Bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on , d > 3, evolving in a potential of the form beta V, where are i.i.d. random variables taking values in [0, + a), and beta > 0. When the potential is integrable, the asymptotic behaviours as beta tends to 0 of the asso ...

Springer Berlin Heidelberg2013

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

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

Deposition Processes with Hardcore Behaviour

Thomas Mountford

Particles are deposited onto a surface with discrete sites. They are subject to an inhibition by which they cannot pass close by a particle already fixed on the surface. This implies that the surface builds up with vertical gaps between the particles. In t ...

Springer US2012

Crossing velocities for an annealed random walk in a random potential

Thomas Mountford

We consider a random walk in an i.i.d. non-negative potential on the d-dimensional integer lattice. The walk starts at the origin and is conditioned to hit a remote location y on the lattice. We prove that the expected time under the annealed path measure ...

2012

The Exact Hausdorff Measure of the Zero Set of Fractional Brownian Motion

Driss Baraka, Thomas Mountford

Let {X(t), t is an element of R-N} be a fractional Brownian motion in R-d of index H. If L(0,I) is the local time of X at 0 on the interval I subset of R-N, then there exists a positive finite constant c(=c(N,d,H)) such that ...

Springer US2011

Lyapunov exponents of Green's functions for random potentials tending to zero

Thomas Mountford

We consider quenched and annealed Lyapunov exponents for the Green's function of -Delta + gamma V, where the potentials V(x) ,x epsilon Z(d), are i.i.d. nonnegative random variables and gamma > 0 is a scalar. We present a probabilistic proof that both Lyap ...

2011

Limit laws of transient excited random walks on integers

Thomas Mountford

We consider excited random walks (ERWs) on Z with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, delta ...

2011

Macroscopic stability for nonfinite range kernels

Thomas Mountford

We extend the strong macroscopic stability introduced in Bramson and Mountford [Ann. Probab. 30 (2002) 1082-1130] for one-dimensional asymmetric exclusion processes with finite range to a large class of one-dimensional conservative attractive models (inclu ...

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

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