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A central limit theorem for Gibbs measures relative to Brownian motion
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  • Published: 11 November 2004

A central limit theorem for Gibbs measures relative to Brownian motion

  • Volker Betz1 &
  • Herbert Spohn2 

Probability Theory and Related Fields volume 131, pages 459–478 (2005)Cite this article

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Abstract.

We study a Gibbs measure over Brownian motion with a pair potential which depends only on the increments. Assuming a particular form of this pair potential, we establish that in the infinite volume limit the Gibbs measure can be viewed as Brownian motion moving in a dynamic random environment. Thereby we are in a position to use the technique of Kipnis and Varadhan and to prove a functional central limit theorem.

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Author information

Authors and Affiliations

  1. Institut für Biomathematik and Biometrie, GSF Forschungszentrum, Postfach 1129, 85758, Neuherberg, Germany

    Volker Betz

  2. Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747, Garching, Germany

    Herbert Spohn

Authors
  1. Volker Betz
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  2. Herbert Spohn
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Corresponding author

Correspondence to Herbert Spohn.

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Cite this article

Betz, V., Spohn, H. A central limit theorem for Gibbs measures relative to Brownian motion. Probab. Theory Relat. Fields 131, 459–478 (2005). https://doi.org/10.1007/s00440-004-0381-8

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  • Received: 21 August 2003

  • Revised: 17 June 2004

  • Published: 11 November 2004

  • Issue Date: March 2005

  • DOI: https://doi.org/10.1007/s00440-004-0381-8

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Limit Theorem
  • Mathematical Biology
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