Hydrodynamic behavior of one dimensional subdiffusive exclusion processes with random conductances

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dc.creatorFaggionato, A.
dc.creatorJara, M.
dc.creatorLandim, C.
dc.date2007-09-03
dc.date.accessioned2026-07-07T08:27:24Z
dc.date.available2026-07-07T08:27:24Z
dc.descriptionConsider a system of particles performing nearest neighbor random walks on the lattice $\ZZ$ 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 $\a$--stable law, $0<\a<1$. This exclusion process models conduction in strongly disordered one-dimensional media. We prove that, when varying over the disorder and for a suitable slowly varying function $L$, under the super-diffusive time scaling $N^{1 + 1/α}L(N)$, the density profile evolves as the solution of the random equation $\partial_t ρ= \mf L_W ρ$, where $\mf L_W$ is the generalized second-order differential operator $\frac d{du} \frac d{dW}$ in which $W$ is a double sided $\a$--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 $\{ξ_{N,x} : x\in\bb Z\}$ having same distribution and fulfilling an a.s. invariance principle. We also prove a law of large numbers for a tagged particle.
dc.identifierhttps://arxiv.org/abs/0709.0306
dc.identifierhttp://arxiv.org/abs/0709.0306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137262
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 60K37, 82C44
dc.titleHydrodynamic behavior of one dimensional subdiffusive exclusion processes with random conductances
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