In this paper we find an upper bound for the probability that a 3 dimensional simple random walk covers each point in a nearest neighbor path connecting 0 and the boundary of an L1 ball of radius N in ℤd. For d ≥ 4, it has been shown in  that such probability decays exponentially with respect to N. For d = 3, however, the same technique does not apply, and in this paper we obtain a slightly weaker upper bound: ∀ε > 0, ∃cε > 0, (Formula Presented).
- 3 dimensional random walk
- Covering probability
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty