Let Sn be a random walk in Zd and let Rn be the range of Sn. We prove an almost sure invariance principle for Rn when d = 3 and a law of the iterated logarithm for Rn when d = 2.
- Almost sure invariance principle
- Intersection local time
- Law of the iterated logarithm
- Range of random walk
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty