Entropy of random walk range

Itai Benjamini, Gady Kozma, Ariel Yadin, Amir Yehudayoff

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd . We show that for d ≥ 3, the entropy is of order n. For d = 2, the entropy is of order n/ log2 n. These values are essentially governed by the size of the boundary of the trace.

Original languageEnglish
Pages (from-to)1080-1092
Number of pages13
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number4
StatePublished - 1 Nov 2010
Externally publishedYes


  • Entropy
  • Random walk

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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