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.
|Number of pages||13|
|Journal||Annales de l'institut Henri Poincare (B) Probability and Statistics|
|State||Published - 1 Nov 2010|
- Random walk
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty