Summary
LetX andY be independent 3-dimensional Brownian motions,X(0)=(0,0,0),Y(0)=(1,0,0) and letp r =P(X[0,r] ⋂Y[0,r]=∅). Then the “non-intersection exponent”\(\mathop {\lim }\limits_{r \to \infty } - {{\log p_{_r } } \mathord{\left/ {\vphantom {{\log p_{_r } } {\log r}}} \right. \kern-\nulldelimiterspace} {\log r}}\) exists and is equal to a similar “non-intersection exponent” for random walks. Analogous results hold inR 2 and for more than 2 paths.
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Supported in part by NSF grant DMS 8702620
Supported by NSF grant DMS 8702879 and an Alfred P. Sloan Research Fellowship
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Burdzy, K., Lawler, G.F. Non-intersection exponents for Brownian paths. Probab. Th. Rel. Fields 84, 393–410 (1990). https://doi.org/10.1007/BF01197892
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DOI: https://doi.org/10.1007/BF01197892