A New Proof of Spitzer's Result on the Winding of Two Dimensional Brownian Motion
Durrett, Richard
Ann. Probab., Tome 10 (1982) no. 4, p. 244-246 / Harvested from Project Euclid
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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.
Publié le : 1982-02-14
Classification:  Brownian motion,  winding,  Cauchy distribution,  Levy's theorem,  60J65,  60F05 
@article{1176993928,
     author = {Durrett, Richard},
     title = {A New Proof of Spitzer's Result on the Winding of Two Dimensional Brownian Motion},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 244-246},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993928}
}

Durrett, Richard. A New Proof of Spitzer's Result on the Winding of Two Dimensional Brownian Motion. Ann. Probab., Tome 10 (1982) no. 4, pp.  244-246. http://gdmltest.u-ga.fr/item/1176993928/