On the behavior of random walk around heavy points

Details On the behavior of random walk around heavy points On the behavior of random walk around heavy points

2006-05-09

arxiv.org/abs/math/0605221v2

Mathematics

Probability

19 pages

Scientific paper

Consider a symmetric aperiodic random walk in $Z^d$, $d\geq 3$. There are
points (called heavy points) where the number of visits by the random walk is
close to its maximum. We investigate the local times around these heavy points
and show that they converge to a deterministic limit as the number of steps
tends to infinity.

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