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Person# Jean-Christophe Mourrat

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In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space.
An elementary example of a random walk is the rando

In probability theory, the central limit theorem (CLT) establishes that, in many situations, for independent and identically distributed random variables, the sampling distribution of the standardiz

In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless), in which case it is known as a numeric

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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 limits are expressed in terms of stable subordinators.

Thomas Mountford, Jean-Christophe Mourrat, Daniel Rodrigues Valesin

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 degree bounded by a given number, the expectation of tau grows exponentially with the number of vertices. Additionally, for any increasing sequence of trees of bounded degree, t divided by its expectation converges in distribution to the unitary exponential distribution. These results also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree, and provide the basis for powerful coarse-graining arguments. To demonstrate this, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett (2009), we show that, for any non-zero infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices. (C) 2016 Elsevier B.V. All rights reserved.

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 occurring, have an effect of the same order of magnitude as the initial medium itself. The main result of the paper is a first-order expansion of the homogenized coefficients, as a function of the perturbation parameter. (C) 2014 Elsevier Masson SAS. All rights reserved.