Brownian charges around loops
type: Item
instance of: scholarly article
title: Brownian charges around loops
zbMATH Open document ID: 0842.60081
DOI: 10.1007/BF01198164
author: Jacques Franchi
author: Yves Le Jan
publication date: 1996-07-22T00:00:00Z
review text: Let \((X^n_t)\) be a Poisson sequence of independent Brownian motions in \(\mathbb{R}^d\), \(d\geq 3\); let \({\mathcal L}\) be a compact oriented submanifold of \(\mathbb{R}^d\), of dimension \(d-2\) and volume \(l\); let \(\Phi_t\) be the sum of the windings of \((X^n_s\), \(0\leq s\leq t)\) around \({\mathcal L}\); then \(\Phi_t/t\) converges in law towards a Cauchy variable of parameter \(l/2\). A similar result is valid when the winding is replaced by the integral of a harmonic 1-form in \(\mathbb{R}^2 \setminus {\mathcal L}\).
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 878016
zbMATH Keywords: Cauchy law
zbMATH Keywords: independent Brownian motions
zbMATH Keywords: winding
MaRDI profile type: Publication
cites work: Théorème des résidus asymptotique pour le mouvement brownien sur une surface riemannienne compacte. (Asymptotic residue theorem for the Brownian motion on a compact Riemannian surface)
cites work: Asymptotic windings of Brownian motion around the windings in a compact Riemannian variety of dimension 3
cites work: Étude asymptotique de certains mouvements browniens complexes avec drift
cites work: Enlacements du Mouvement Brownien Autour Des Courbes de L'Espace
cites work: Winding of the plane Brownian motion
cites work: Further asymptotic laws of planar Brownian motion
cites work: Some Theorems Concerning 2-Dimensional Brownian Motion
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 878016