Nonintersecting Planar Brownian Motions
نویسنده
چکیده
In this paper we construct a measure on pairs of Brownian motions starting at the same point conditioned so their paths do not intersect. The construction of this measure is a start towards the rigorous understanding of nonintersecting Brownian motions as a conformal eld. Let B 1 ; B 2 be independent Brownian motions in R 2 starting at distinct points on the unit circle. Let T j r be the rst time that the jth Brownian motion reaches distance r and let D r be the event D r = fB 1 0; T 1 e r ] \ B 2 0; T 2 e r ] = ;g: We construct the measure by considering the limit of the measure induced by Brownian motions conditioned on the event D r .
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