For a sequence of i.i.d. random variables {ξx: x∈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 ξx. We examine a quenched non-equilibrium 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].
Publié le : 2008-04-15
Classification:
Hydrodynamic limit,
Tagged particle,
Non-equilibrium fluctuations,
Random environment,
Fractional Brownian motion,
60K35
@article{1207948223,
author = {Jara, M. D. and Landim, C.},
title = {Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 341-361},
language = {en},
url = {http://dml.mathdoc.fr/item/1207948223}
}
Jara, M. D.; Landim, C. Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 341-361. http://gdmltest.u-ga.fr/item/1207948223/