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dc.contributor.authorBurdzy, Krzysztof
dc.contributor.authorLawler, Gregory F.
dc.date.accessioned2005-11-18T18:05:31Z
dc.date.available2005-11-18T18:05:31Z
dc.date.issued1990-07
dc.identifier.citationBurdzy, K. & G.F. Lawler. (1990). Non-intersection exponents for Brownian paths. Part II: Estimates and applications to a random fractal. The Annals of Probability, 18(3), 981-1009.en
dc.identifier.urihttp://hdl.handle.net/1773/2167
dc.description.abstractLet X and Y be independent two-dimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a closed loop around 0}. Asymptotic estimates (when [epsilon] --> 0) of p([epsilon]); q([epsilon]), and some related probabilities, are given. Let F be the boundary of the unbounded connected component of [the set of real numbers squared]\Z[0; 1], where Z(t) = X(t) - tX(1) for t [is an element of the set] [0; 1]. Then F is a closed Jordan arc and the Hausdorff dimension of F is less or equal to 3/2 - 1=(4[pi squared]).en
dc.description.sponsorshipKrzysztof Burdzy was supported in part by NSF grant DMS 8702620. Gregory F. Lawler was supported by NSF grant DMS 8702879 and an Alfred P. Sloan Research Fellowship.en
dc.format.extent289429 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectBrownian motionen
dc.subjectfractalen
dc.subjectintersections of Brownian pathsen
dc.subjectcritical exponentsen
dc.titleNon-intersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal.en
dc.title.alternativeBrownian intersection exponentsen
dc.typeArticleen


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