Brownian charges around loops

J. Franchi; Y. Le Jan

doi:10.1007/BF01198164

Brownian charges around loops

J. Franchi, Y. Le Jan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (Xⁿ_t ) be a Poisson sequence of independent Brownian motions in double-struck R sign^d, d ≧ 3; Let ℒ be a compact oriented submanifold of double-struck R sign^d, of dimension d - 2 and volume ℓ; let Φ_t, be the sum of the windings of (Xⁿ_s, 0 ≦ s ≦ t) around ℒ; then Φ_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 double-struck R sign^d\ℒ.

Original language	English (US)
Pages (from-to)	501-514
Number of pages	14
Journal	Probability Theory and Related Fields
Volume	104
Issue number	4
DOIs	https://doi.org/10.1007/BF01198164
State	Published - Apr 1996

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF01198164

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title = "Brownian charges around loops",

abstract = "Let (Xnt ) be a Poisson sequence of independent Brownian motions in double-struck R signd, d ≧ 3; Let ℒ be a compact oriented submanifold of double-struck R signd, of dimension d - 2 and volume ℓ; let Φt, be the sum of the windings of (Xns, 0 ≦ s ≦ t) around ℒ; then Φt/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 double-struck R signd\ℒ.",

author = "J. Franchi and {Le Jan}, Y.",

year = "1996",

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doi = "10.1007/BF01198164",

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AU - Franchi, J.

AU - Le Jan, Y.

PY - 1996/4

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N2 - Let (Xnt ) be a Poisson sequence of independent Brownian motions in double-struck R signd, d ≧ 3; Let ℒ be a compact oriented submanifold of double-struck R signd, of dimension d - 2 and volume ℓ; let Φt, be the sum of the windings of (Xns, 0 ≦ s ≦ t) around ℒ; then Φt/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 double-struck R signd\ℒ.

AB - Let (Xnt ) be a Poisson sequence of independent Brownian motions in double-struck R signd, d ≧ 3; Let ℒ be a compact oriented submanifold of double-struck R signd, of dimension d - 2 and volume ℓ; let Φt, be the sum of the windings of (Xns, 0 ≦ s ≦ t) around ℒ; then Φt/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 double-struck R signd\ℒ.

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Brownian charges around loops

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