Self-intersections of 1-dimensional random walks |
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Authors: | David J Aldous |
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Institution: | (1) Department of Statistics, University of California, 94720 Berkeley, CA, USA |
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Abstract: | Summary Consider a random walk S
n
on the integers, where the steps
i
have mean 0 and variance 2. Let T be the time of first self-intersection of the random walk. It is shown that, as ![sgr](/content/n021612t18g30013/xxlarge963.gif) ![rarr](/content/n021612t18g30013/xxlarge8594.gif) , T grows at rate 2/3. More precisely, T 2/3 has a non-degenerate limit distribution which can be described in terms of Brownian motion local time.Research supported by National Science Foundation Grant MCS80-02698. |
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Keywords: | |
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