1,452 research outputs found
Law of large numbers for non-elliptic random walks in dynamic random environments
We prove a law of large numbers for a class of -valued random walks in
dynamic random environments, including non-elliptic examples. We assume for the
random environment a mixing property called \emph{conditional cone-mixing} and
that the random walk tends to stay inside wide enough space-time cones. The
proof is based on a generalization of a regeneration scheme developed by Comets
and Zeitouni for static random environments and adapted by Avena, den Hollander
and Redig to dynamic random environments. A number of one-dimensional examples
are given. In some cases, the sign of the speed can be determined.Comment: 36 pages, 4 figure
Stretched Exponential Relaxation in the Biased Random Voter Model
We study the relaxation properties of the voter model with i.i.d. random
bias. We prove under mild condions that the disorder-averaged relaxation of
this biased random voter model is faster than a stretched exponential with
exponent , where depends on the transition rates
of the non-biased voter model. Under an additional assumption, we show that the
above upper bound is optimal. The main ingredient of our proof is a result of
Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe
Berman-Konsowa principle for reversible Markov jump processes
In this paper we prove a version of the Berman\tire Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman\tire Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability measures for random finite paths from one set to the other, the other involving a class of finite unit flows from one set to the other. The Berman\tire Konsowa principle complements the Dirichlet principle and the Thomson principle, and turns out to be especially useful for obtaining sharp estimates on crossover times in metastable interacting particle systems
A crossover for the bad configurations of random walk in random scenery
Article / Letter to editorMathematisch Instituu
The parabolic Anderson model on a Galton-Watson tree
We study the long-time asymptotics of the total mass of the solution to the
parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree
with bounded degrees. We identify the second-order contribution to this
asymptotics in terms of a variational formula that gives information about the
local structure of the region where the solution is concentrated. The analysis
behind this formula suggests that, under mild conditions on the model
parameters, concentration takes place on a tree with minimal degree. Our
approach can be applied to finite locally tree-like random graphs, in a coupled
limit where both time and graph size tend to infinity. As an example, we
consider the configuration model or, more precisely, the uniform simple random
graph with a prescribed degree sequence.Comment: 32 page
Minimum entropy production principle from a dynamical fluctuation law
The minimum entropy production principle provides an approximative
variational characterization of close-to-equilibrium stationary states, both
for macroscopic systems and for stochastic models. Analyzing the fluctuations
of the empirical distribution of occupation times for a class of Markov
processes, we identify the entropy production as the large deviation rate
function, up to leading order when expanding around a detailed balance
dynamics. In that way, the minimum entropy production principle is recognized
as a consequence of the structure of dynamical fluctuations, and its
approximate character gets an explanation. We also discuss the subtlety
emerging when applying the principle to systems whose degrees of freedom change
sign under kinematical time-reversal.Comment: 17 page
Binary data corruption due to a Brownian agent
We introduce a model of binary data corruption induced by a Brownian agent
(active random walker) on a d-dimensional lattice. A continuum formulation
allows the exact calculation of several quantities related to the density of
corrupted bits \rho; for example the mean of \rho, and the density-density
correlation function. Excellent agreement is found with the results from
numerical simulations. We also calculate the probability distribution of \rho
in d=1, which is found to be log-normal, indicating that the system is governed
by extreme fluctuations.Comment: 39 pages, 10 figures, RevTe
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