Person
Thomas Mountford
Related publications (34)
A construction of the Stable Web
We provide a process on the space of collections of coalescing cadlag stable paths and show convergence in an appropriate topology for coalescing stable random walks on the integer lattice. ...
IMPA2019Exponential 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 Bv2016Functional 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 ...
Impa2016Lyapunov 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 Mathematics2015Random walks generated by equilibrium contact processes
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 Mathematics2015Supercriticality conditions for asymmetric zero-range process with sitewise disorder
We discuss necessary and sufficient conditions for the convergence of disordered asymmetric zero-range process to the critical invariant measure. ...
Brazilian Statistical Association2015Metastable 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 Mathematics2013Ergodic 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 Statistics2013Supercriticality 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 Mathematics2013Lyapunov 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