PLANAR BROWNIAN MOTION WINDS EVENLY ALONG ITS TRAJECTORY
Résumé
Let D_N be the set of points around which a planar Brownian motion winds at least N times. We prove that the random measure on the plane with density 2πN D_N with respect to the Lebesgue measure converges almost surely weakly, as N tends to infinity, towards the occupation measure of the Brownian motion.
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