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Entropy of random walk range

Itai Benjamini;  Gady Kozma;  Ariel Yadin;  Amir Yehudayoff — 2010

Annales de l'I.H.P. Probabilités et statistiques

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

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