Abstract. It is well known that the maximal displacement of a random walk indexed by an m-ary tree with bounded i.i.d. edge-weights can reliably yield much larger asymptotics than a classical random walk whose summands are drawn from the same distribution. Presently we show that if the edge-weights are mean-zero, then nonclassical asymptotics arise even when the tree grows much more slowly than subexponentially. Our conditions are stated in terms of a Minkowski-type logarithmic dimension of the boundary of the tree.
Keywords. Optimal reward, tree-indexed random walks, logarithmic dimension.
AMS Classification (2000). 60G50, 05C05.
Support. Research supported in part by grants from the U.S. National Science Foundation.
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Davar Khoshnevisan Department of Mathematics University of Utah 155 S, 1400 E JWB 233 Salt Lake City, UT 84112-0090, U.S.A. davar@math.utah.edu |
Thomas M. Lewis Department of Mathematics Furman University Greenville, SC 29613, U.S.A. tom.lewis@math.furman.edu |
Last Update: July 22, 2002
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2002 - Davar Khoshnevisan and Thomas M. Lewis