Entropy of Random Walk Range

Details Entropy of Random Walk Range Entropy of Random Walk Range

2009-03-18

arxiv.org/abs/0903.3179v1

Mathematics

Probability

Scientific paper

We study the entropy of the set traced by an $n$-step random walk on $\Z^d$.
We show that for $d \geq 3$, the entropy is of order $n$. For $d = 2$, the
entropy is of order $n/\log^2 n$. These values are essentially governed by the
size of the boundary of the trace.

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