5,014 research outputs found
The need for speed : Maximizing random walks speed on fixed environments
We study nearest neighbor random walks on fixed environments of
composed of two point types : and for . We show
that for every environment with density of drifts bounded by we
have , where
is a random walk on the environment. In addition up to some integer effect the
environment which gives the best speed is given by equally spaced drifts
Geometry of the random interlacement
We consider the geometry of random interlacements on the -dimensional
lattice. We use ideas from stochastic dimension theory developed in
\cite{benjamini2004geometry} to prove the following: Given that two vertices
belong to the interlacement set, it is possible to find a path between
and contained in the trace left by at most
trajectories from the underlying Poisson point process. Moreover, this result
is sharp in the sense that there are pairs of points in the interlacement set
which cannot be connected by a path using the traces of at most trajectories
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