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Probability Seminar by Balint Virag
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**PROBABILITY SEMINAR **

Brownian beads

Balint Virag
Abstract: Two-dimensional stochastic models are of great interest to
physicists and probabilists because they reflect the rich world of
conformal symmetries. We consider the simplest of these models, planar
Brownian motion. Two and three are the only dimensions where Brownian
motion has cut-times, that is times at which past and future paths are
disjoint. Brownian beads are the sections of the path in between the
cut-times. We show that these beads are independent of each other (after a
conformal transformation) and planar Brownian motion can be "stringed" out
of them in the same way that Brownian motion on the line is constructed
from excursions.