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Brownian charges around loops
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  • Published: December 1996

Brownian charges around loops

  • J. Franchi1,2 &
  • Y. Le Jan3 

Probability Theory and Related Fields volume 104, pages 501–514 (1996)Cite this article

  • 66 Accesses

  • 2 Citations

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Summary

Let (X n t ) be a Poisson sequence of independent Brownian motions in ℝd,d≧3; Let ℒ be a compact oriented submanifold of ℝd, of dimensiond−2 and volume ℓ; let Φt be the sum of the windings of (X n s , 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 ℝd∖ℒ.

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References

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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris 6, 4 place Jussieu, Tour 56, 3ème étage, F-75252, Paris Cedex 05, France

    J. Franchi

  2. Université Paris-Val de Marne, 61 avenue De Gaulle, F-94010, Créteil, France

    J. Franchi

  3. Université Paris-Sud, Bâtiment 425, F-91405, Orsay Cedex, France

    Y. Le Jan

Authors
  1. J. Franchi
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  2. Y. Le Jan
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Cite this article

Franchi, J., Le Jan, Y. Brownian charges around loops. Probab. Th. Rel. Fields 104, 501–514 (1996). https://doi.org/10.1007/BF01198164

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  • Received: 27 June 1994

  • Revised: 14 September 1995

  • Issue Date: December 1996

  • DOI: https://doi.org/10.1007/BF01198164

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Mathematics Subject Classification (1991)

  • 60J65
  • 60H05
  • 60F05
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