Entropy of Random Walk Range

Itai Benjamini; Gady Kozma; Ariel Yadin; Amir Yehudayoff

doi:10.1214/09-AIHP345

Entropy of Random Walk Range

Probability 2015-05-13 v1 Combinatorics

Authors: 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.

Keywords

random walk in random environment random walks random walk on graphs

Cite

@article{arxiv.0903.3179,
  title  = {Entropy of Random Walk Range},
  author = {Itai Benjamini and Gady Kozma and Ariel Yadin and Amir Yehudayoff},
  journal= {arXiv preprint arXiv:0903.3179},
  year   = {2015}
}

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