On covering paths with 3 dimensional random walk

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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).

Original languageEnglish
Article number57
JournalElectronic Communications in Probability
StatePublished - 2018
Externally publishedYes


  • 3 dimensional random walk
  • Covering probability

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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