Hydrodynamic limit of a d-dimensional exclusion process with conductances

Valentim, Fábio Júlio. "Hydrodynamic limit of a d-dimensional exclusion process with conductances." Annales de l'I.H.P. Probabilités et statistiques 48.1 (2012): 188-211. <http://eudml.org/doc/272035>.

@article{Valentim2012,
abstract = {Fix a polynomial Φ of the form Φ(α) = α + ∑2≤j≤m  aj  αk=1j with Φ'(1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on $\{\mathbb \{T\}\}^\{d\}$ , with conductances given by special class of functionsW, is described by the unique weak solution of the non-linear parabolic partial differential equation ∂tρ = ∑d  ∂xk  ∂Wk  Φ(ρ). We also derive some properties of the operator ∑k=1d  ∂xk  ∂Wk.},
author = {Valentim, Fábio Júlio},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {exclusion processes; random conductances; hydrodynamic limit},
language = {eng},
number = {1},
pages = {188-211},
publisher = {Gauthier-Villars},
title = {Hydrodynamic limit of a d-dimensional exclusion process with conductances},
url = {http://eudml.org/doc/272035},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Valentim, Fábio Júlio
TI - Hydrodynamic limit of a d-dimensional exclusion process with conductances
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 1
SP - 188
EP - 211
AB - Fix a polynomial Φ of the form Φ(α) = α + ∑2≤j≤m  aj  αk=1j with Φ'(1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on ${\mathbb {T}}^{d}$ , with conductances given by special class of functionsW, is described by the unique weak solution of the non-linear parabolic partial differential equation ∂tρ = ∑d  ∂xk  ∂Wk  Φ(ρ). We also derive some properties of the operator ∑k=1d  ∂xk  ∂Wk.
LA - eng
KW - exclusion processes; random conductances; hydrodynamic limit
UR - http://eudml.org/doc/272035
ER -