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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 inx⩾y⩾z. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Drexel University, 19104, Philadelphia, Pennsylvania

    Jet Wimp & Doron Zeilberger

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  1. Jet Wimp
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  2. Doron Zeilberger
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Wimp, J., Zeilberger, D. How likely is Polya's drunkard to stay in x⩾ y⩾z?. J Stat Phys 57, 1129–1135 (1989). https://doi.org/10.1007/BF01020052

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  • DOI: https://doi.org/10.1007/BF01020052

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