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February, 1982 A New Proof of Spitzer's Result on the Winding of Two Dimensional Brownian Motion
Richard Durrett
Ann. Probab. 10(1): 244-246 (February, 1982). DOI: 10.1214/aop/1176993928

Abstract

Let $W(t)$ be a two dimensional Brownian motion with $W(0) = (1, 0)$ and let $\varphi(t)$ be the net number of times the path has wound around (0, 0), counting clockwise loops as $-1$, counterclockwise as $+1$. Spitzer has shown that as $t \rightarrow \infty, 4\pi\varphi(t)/\log t$ converges to a Cauchy distribution with parameter 1. In this paper we will use Levy's result on the conformal invariance of Brownian motion to give a simple proof of Spitzer's theorem.

Citation

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Richard Durrett. "A New Proof of Spitzer's Result on the Winding of Two Dimensional Brownian Motion." Ann. Probab. 10 (1) 244 - 246, February, 1982. https://doi.org/10.1214/aop/1176993928

Information

Published: February, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0479.60081
MathSciNet: MR637391
Digital Object Identifier: 10.1214/aop/1176993928

Subjects:
Primary: 60J65
Secondary: 60F05

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 1 • February, 1982
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