Brownian charges around loops

J. Franchi, Y. Le Jan

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)501-514
Number of pages14
JournalProbability Theory and Related Fields
Volume104
Issue number4
DOIs
StatePublished - Apr 1996

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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