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Small Mass Limit of a Langevin Equation on a Manifold

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Abstract

We study damped geodesic motion of a particle of mass m on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as \({m \to 0}\), its solutions converge to solutions of a limiting equation which includes a noise-induced drift term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Jeremiah Birrell & Jan Wehr

  2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Scott Hottovy

  3. Soft Matter Lab, Department of Physics, Bilkent University, Ankara, 06800, Turkey

    Giovanni Volpe

  4. UNAM, National Nanotechnology Research Center, Bilkent University, Ankara, 06800, Turkey

    Giovanni Volpe

Authors
  1. Jeremiah Birrell
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  2. Scott Hottovy
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  3. Giovanni Volpe
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  4. Jan Wehr
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Corresponding author

Correspondence to Jeremiah Birrell.

Additional information

Communicated by Christian Maes.

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Birrell, J., Hottovy, S., Volpe, G. et al. Small Mass Limit of a Langevin Equation on a Manifold. Ann. Henri Poincaré 18, 707–755 (2017). https://doi.org/10.1007/s00023-016-0508-3

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  • DOI: https://doi.org/10.1007/s00023-016-0508-3

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