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Optimal reward on a sparse tree with random edge weights

Part of: Stochastic processes Graph theory

Published online by Cambridge University Press:  14 July 2016

Davar Khoshnevisan  and
Thomas M. Lewis
Davar Khoshnevisan*
Affiliation:
University of Utah
Thomas M. Lewis*
Affiliation:
Furman University
*
∗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: [email protected]
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Abstract

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.

Keywords

Optimal rewardtree-indexed random walklogarithmic dimension

MSC classification

Primary: 60G50: Sums of independent random variables; random walks 05C05: Trees
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 926 - 945
Copyright
Copyright © Applied Probability Trust 2003 

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