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Intersections of random walks in four dimensions. II

Authors:	Gregory F Lawler

Institution:	(1) Department of Mathematics, Duke University, 27706 Durham, NC, USA

Abstract:	Letf(n) be the probability that the paths of two simple random walks of lengthn starting at the origin in ⁴ have no intersection. It has previously been shown thatf(n)c(logn)^–1/2. Here it is proved that for allr>1/2, $\mathop {\lim }\limits_{n \to \infty } (\log n)^r f(n) = \infty$ .Research Supported by NSF grant MCS-8301037

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