Quenched Nonequilibrium Central Limit Theorem for a Tagged Particle in the Exclusion Process with Bond Disorder

For a sequence of i.i.d. random variables {ξx : x ∈ Z} bounded above and below by strictly positive finite constants, consider the nearestneighbor one-dimensional simple exclusion process in which a particle at x (resp. x + 1) jumps to x + 1 (resp. x) at rate ξx. We examine a quenched nonequilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder {ξx : x ∈ Z}. We prove that the position of the tagged particle converges under diffusive scaling to a Gaussian process if the other particles are initially distributed according to a Bernoulli product measure associated to a smooth profile ρ0 : R → [0, 1].