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Hydrodynamic limit for a system of independent, sub-ballistic random walks in a common random environment | | Milton Jara
; Jonathon Peterson
; | | Date: |
17 Oct 2014 | | Abstract: | We consider a system of independent random walks in a common random
environment. Previously, a hydrodynamic limit for the system of RWRE was proved
under the assumption that the random walks were transient with positive speed.
In this paper we instead consider the case where the random walks are transient
but with a sublinear speed of the order $n^kappa$ for some $kappa in (0,1)$
and prove a quenched hydrodynamic limit for the system of random walks with
time scaled by $n^{1/kappa}$ and space scaled by $n$. The most interesting
feature of the hydrodynamic limit is that the influence of the environment does
not average out under the hydrodynamic scaling; that is, the asymptotic
particle density depends on the specific environment chosen. The hydrodynamic
limit for the system of RWRE is obtained by first proving a hydrodynamic limit
for a system of independent particles in a directed trap environment. | | Source: | arXiv, 1410.4832 | | Services: | Forum | Review | PDF | Favorites | |
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