Abstract
We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Itô’s excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint. The index is computed and equals 1/2.
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Research partially supported by NSF grant #DMS-0206781.
Mathematics Subject Classification (2000): 60J65; 30C35
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Virág, B. Brownian beads. Probab. Theory Relat. Fields 127, 367–387 (2003). https://doi.org/10.1007/s00440-003-0289-8
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DOI: https://doi.org/10.1007/s00440-003-0289-8