How likely is Polya's drunkard to stay in x≥ y≥z?

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Abstract

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay in x≥y≥z. It is shown that his probability of returning to the origin and staying in the allowed region is %6.4844....

Original languageEnglish (US)
Pages (from-to)1129-1135
Number of pages7
JournalJournal of Statistical Physics
Volume57
Issue number5-6
DOIs
StatePublished - Dec 1 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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