A central limit theorem for random walks in random labyrinths
A central limit theorem for the asymmetric simple exclusion process
A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington-Kirkpatrick model.
A comprehensive proof of localization for continuous Anderson models with singular random potentials
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution),...
A deterministic displacement theorem for Poisson processes.
A dynamical characterization of Poisson-Dirichlet distributions.
A generalized Biane process
A large deviation result for the subcritical Bernoulli percolation
A lattice gas model for the incompressible Navier–Stokes equation
We recover the Navier–Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier–Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.
A lower bound for time correlation of lattice gases.
A microscopic model for the Burgers equation and longest increasing subsequences.
A monotonicity result for hard-core and Widom-Rowlinson models on certain -dimensional lattices.
A nonasymptotic theorem for unnormalized Feynman–Kac particle models
We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...
A note on limiting behaviour of disastrous environment exponents.
A note on percolation on : isoperimetric profile via exponential cluster repulsion.
A note on Talagrand's positivity principle.
A note on the diffusive scaling limit for a class of linear systems.
A PDE approach to certain large deviation problems for systems of parabolic equations
A percolation formula.
A simple example concerning the global Markov Property of lattice random fields