On covering paths with 3 dimensional random walk Academic Article uri icon

abstract

  • © 2018, University of Washington. All rights reserved. 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 [5] 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).

author list (cited authors)

  • Procaccia, E. B., & Zhang, Y.

complete list of authors

  • Procaccia, Eviatar B||Zhang, Yuan

publication date

  • January 2018