Publications de Jean-Christophe Mourrat

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

Aging of asymmetric dynamics on the random energy model

Jean-Christophe Mourrat

We show aging of Glauber-type dynamics on the random energy model, inthe sense that we obtain the annealed scaling limits of the clock process and of theage process. The latter encodes the Gibbs weight of the configuration occupied by thedynamics. Both lim ...

Springer2015

First-order expansion of homogenized coefficients under Bernoulli perturbations

Jean-Christophe Mourrat

Divergence-form operators with stationary random coefficients homogenize over large scales. We investigate the effect of certain perturbations of the medium on the homogenized coefficients. The perturbations considered are rare at the local level, but when ...

Gauthier-Villars/Editions Elsevier2015

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

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Jean-Christophe Mourrat

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...

Springer Heidelberg2014

On the rate of convergence in the martingale central limit theorem

Jean-Christophe Mourrat

Consider a discrete-time martingale, and let V-2 be its normalized quadratic variation. As V-2 approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian distribution. For any ...

Int Statistical Inst2013

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

Quantitative Version Of The Kipnis-Varadhan Theorem And Monte Carlo Approximation Of Homogenized Coefficients

Jean-Christophe Mourrat

This article is devoted to the analysis of a Monte Carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. We consider the case of independent and identically distributed coefficients, and adopt the p ...

Inst Mathematical Statistics2013

A quantitative central limit theorem for the random walk among random conductances

Jean-Christophe Mourrat

We consider the random walk among random conductances on Z(d). We assume that the conductances are independent, identically distributed and uniformly bounded away from 0 and infinity. We obtain a quantitative version of the central limit theorem for this r ...

Univ Washington, Dept Mathematics2012