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Sticky flows on the circle and their noises
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  • Published: 02 February 2004

Sticky flows on the circle and their noises

  • Yves Le Jan1 &
  • Olivier Raimond1 

Probability Theory and Related Fields volume 129, pages 63–82 (2004)Cite this article

  • 182 Accesses

  • 14 Citations

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Abstract.

This paper gives a construction of sticky flows on the circle. Sticky flows give examples of stochastic flows of kernels that interpolates between Arratia’s coalescing flow and the deterministic diffusion flow. They are associated with systems of sticky independent Brownian particles on the circle, for some fixed parameter of stickyness. It is proved that the noise generated by Brownian sticky flows is black. A new proof of the fact that the noise of Arratia’s coalescing flow is black is given.

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References

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  4. Le Jan, Y., Raimond, O.: Flows, coalescence and noise. math.PR/0203221, To appear in The Annals of Probability

  5. Le Jan, Y., Raimond, O.: Sticky flows on the circle. arXiv:math.PR/0211387, 2002

  6. Le Jan, Y., Raimond, O.: The noise of a Brownian sticky flow is black. arXiv:math.PR/0212269, 2002

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Author information

Authors and Affiliations

  1. Département de Mathématiques, Bâtiment, 425, Université Paris-Sud, 91405, Orsay Cedex, France

    Yves Le Jan & Olivier Raimond

Authors
  1. Yves Le Jan
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  2. Olivier Raimond
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Correspondence to Olivier Raimond.

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Cite this article

Jan, Y., Raimond, O. Sticky flows on the circle and their noises. Probab. Theory Relat. Fields 129, 63–82 (2004). https://doi.org/10.1007/s00440-003-0324-9

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  • Received: 17 June 2003

  • Revised: 09 September 2003

  • Published: 02 February 2004

  • Issue Date: May 2004

  • DOI: https://doi.org/10.1007/s00440-003-0324-9

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Keywords

  • Fixed Parameter
  • Brownian Particle
  • Diffusion Flow
  • Stochastic Flow
  • Deterministic Diffusion
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