Thierry Bodineau

Current Large Deviations for Asymmetric Exclusion Processes with Open Boundaries

We study the large deviation functional of the current for the Weakly Asymmetric Simple Exclusion Process in contact with two reservoirs. We compare this functional in the large drift limit to the one of the Totally Asymmetric Simple Exclusion Process, in particular to the Jensen-Varadhan functional. Conjectures for generalizing the Jensen-Varadhan functional to open systems are also stated.

Large deviations in the van der Waals limit

In this paper we extend the analysis in Benois et al. (Markov Process. Rel. Fields (1997) 175-198) by proving a strong large deviation principle for the empirical distribution of Ising spins in dimensions when the interaction is determined by a Kac potential and the temperature is below the critical value.

Some new results on the kinetic Ising model in a pure phase

AbstractWe consider a general class of Glauber dynamics reversible with respect to the standard Ising model in ℤd with zero external field and inverse temperature β strictly larger than the critical value βc in dimension 2 or the so called “slab threshold” β in dimension d ≥ 3. We first prove that the inverse spectral gap in a large cube of side N with plus boundary conditions is, apart from logarithmic corrections, larger than N in d = 2 while the logarithmic Sobolev constant is instead larger than N2 in any dimension. Such a result substantially improves over all the previous existing bounds and agrees with a similar computations obtained in the framework of a one dimensional toy model based on mean curvature motion. The proof, based on a suggestion made by H. T. Yau some years ago, explicitly constructs a subtle test function which forces a large droplet of the minus phase inside the plus phase. The relevant bounds for general d ≥ 2 are then obtained via a careful use of the recent

Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats

\mathbb{L}^{1}

Copolymers at Selective Interfaces: New Bounds on the Phase Diagram

–approach to the Wulff construction. Finally we prove that in d = 2 the probability that two independent initial configurations, distributed according to the infinite volume plus phase and evolving under any coupling, agree at the origin at time t is bounded from below by a stretched exponential

Lyapunov functionals for boundary-driven nonlinear drift–diffusion equations

\exp ( - \sqrt t )