arXiv subjects
Publications and source records attributed to M. D. Jara.
We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation.
For interacting particle systems that satisfies the gradient condition, the hydrodynamic limit and the equilibrium fluctuations are well known. We prove that under the presence of a symmetric random environment, these scaling limits also hold for almost every choice of the environment, with homogenized coefficients that does not depend on the particular realization of the random environment.
We obtain the equilibrium fluctuations for the empirical density of particles for the zero-range process in the Sierpinski gasket. The limiting process is a generalized Ornstein-Uhlenbeck process generated by the Neumann Laplacian and its corresponding Dirichlet form on the gasket.
For a sequence of i.i.d. random variables $\{ξ_x : x\in \bb Z\}$ bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at $x$ (resp. $x+1$) jumps to $x+1$ (resp. $x$) at rate $ξ_x$. We examine a quenched nonequilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder $\{ξ_x : x\in \bb Z\}$. 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 $ρ_0:\bb R\to [0,1]$.
We prove a nonequilibirum central limit theorem for the position of a tagged particle in the one-dimensional nearest-neighbor symmetric simple exclusion process under diffusive scaling starting from a Bernoulli product measure associated to a smooth profile $ρ_0:\bb R\to [0,1]$.