Hydrodynamic behavior of 1D subdiffusive exclusion processes with random conductances
成果类型：
Article
署名作者：
Faggionato, A.; Jara, M.; Landim, C.
署名单位：
Sapienza University Rome; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-008-0157-7
发表日期：
2009
页码：
633-667
关键词：
摘要：
Consider a system of particles performing nearest neighbor random walks on the lattice Z under hard-core interaction. The rate for a jump over a given bond is direction-independent and the inverse of the jump rates are i.i.d. random variables belonging to the domain of attraction of an alpha-stable law, 0 < alpha < 1. This exclusion process models conduction in strongly disordered 1D media. We prove that, when varying over the disorder and for a suitable slowly varying function L, under the super-diffusive time scaling N1+1/alpha L(N), the density profile evolves as the solution of the random equation. partial derivative(t)rho = L-W rho, where L-W is the generalized second-order differential operator d/du d/dW in which W is a double-sided alpha-stable subordinator. This result follows from a quenched hydrodynamic limit in the case that the i.i.d. jump rates are replaced by a suitable array {xi(N,x) : x is an element of Z} having same distribution and fulfilling
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