Tertuliano Franco

Phase transition of a heat equation with Robin’s boundary conditions and exclusion process

For a heat equation with Robin’s boundary conditions which depends on a parameter α > 0, we prove that its unique weak solution ρα converges, when α goes to zero or to infinity, to the unique weak solution of the heat equation with Neumann’s boundary conditions or the heat equation with periodic boundary conditions, respectively. To this end, we use uniform bounds on a Sobolev norm of ρα obtained from the hydrodynamic limit of the symmetric slowed exclusion process, plus a careful analysis of boundary terms.

Crossover to the Stochastic Burgers Equation for the WASEP with a Slow Bond

We consider the weakly asymmetric simple exclusion process in the presence of a slow bond and starting from the invariant state, namely the Bernoulli product measure of parameter

Hydrodynamical behavior of symmetric exclusion with slow bonds

{\rho \in (0,1)}

Large deviations for the exclusion process with a slow bond

ρ∈(0,1). The rate of passage of particles to the right (resp. left) is

Hydrodynamic Limit of Quantum Random Walks

{\frac{1}{2} + \frac{a}{2n^{\gamma}}}

A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time

12+a2nγ (resp.