Abstract
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 language | English |
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Pages (from-to) | 1080-1092 |
Number of pages | 13 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 46 |
Issue number | 4 |
DOIs | |
State | Published - 1 Nov 2010 |
Externally published | Yes |
Keywords
- Entropy
- Random walk
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty