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Cut Times for Simple Random Walk
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Gregory F. Lawler, Duke University and Cornell University
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Abstract
Let $S(n)$ be a simple random walk taking values in $Z^d$. A
time $n$ is called a cut time if
[ S[0,n] cap S[n+1,infty) = emptyset . ]
We show that in three dimensions the number of cut times less than
$n$ grows like $n^{1 - zeta}$ where $zeta = zeta_d$ is the intersection
exponent. As part of the proof we show that in two
or three dimensions
[ P{S[0,n] cap S[n+1,2n] = emptyset } asymp n^{-zeta}, ]
where $asymp$ denotes that each side is bounded by a constant times
the other side.
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Full text: PDF
Pages: 1-24
Published on: October 19, 1996
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Electronic Journal of Probability. ISSN: 1083-6489 |
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