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arXiv · 0903.3179

Entropy of Random Walk Range

Itai Benjamini·Gady Kozma·Ariel Yadin·Amir Yehudayoff
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Abstract

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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Itai Benjamini, Gady Kozma, Ariel Yadin, Amir Yehudayoff. 2009-03-18. Entropy of Random Walk Range. https://doi.org/10.1214/09-aihp345

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