Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder

M. D. Jara; C. Landim

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 2, page 341-361
  • ISSN: 0246-0203

Abstract

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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].

How to cite

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Jara, M. D., and Landim, C.. "Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder." Annales de l'I.H.P. Probabilités et statistiques 44.2 (2008): 341-361. <http://eudml.org/doc/77973>.

@article{Jara2008,
abstract = {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].},
author = {Jara, M. D., Landim, C.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {hydrodynamic limit; tagged particle; non-equilibrium fluctuations; random environment; fractional brownian motion; non-equilibrium; fractional Brownian motion.},
language = {eng},
number = {2},
pages = {341-361},
publisher = {Gauthier-Villars},
title = {Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder},
url = {http://eudml.org/doc/77973},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Jara, M. D.
AU - Landim, C.
TI - Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 2
SP - 341
EP - 361
AB - 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].
LA - eng
KW - hydrodynamic limit; tagged particle; non-equilibrium fluctuations; random environment; fractional brownian motion; non-equilibrium; fractional Brownian motion.
UR - http://eudml.org/doc/77973
ER -

References

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