zbMATH — the first resource for mathematics

Brownian beads. (English) Zbl 1035.60085
Summary: 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.

60J65 Brownian motion
30C35 General theory of conformal mappings
Full Text: DOI arXiv