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Optimal reward on a sparse tree with random edge weights

  • Davar Khoshnevisan (a1) and Thomas M. Lewis (a2)


It is well known that the maximal displacement of a random walk indexed by an m-ary tree with bounded independent and identically distributed edge weights can reliably yield much larger asymptotics than a classical random walk whose summands are drawn from the same distribution. We show that, if the edge weights are mean-zero, then nonclassical asymptotics arise even when the tree grows much more slowly than exponentially. Our conditions are stated in terms of a Minkowski-type logarithmic dimension of the boundary of the tree.


Corresponding author

Postal address: Department of Mathematics, University of Utah, Salt Lake City, UT 84112–0090, USA.
∗∗ Postal address: Department of Mathematics, Furman University, Greenville, SC 29613, USA. Email address:


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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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