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The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction

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Abstract

A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.

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Acknowledgments

DH and SH would like to acknowledge support from Drake University and Iowa State University. GV was partially funded by a Marie Curie Career Integration Grant (PCIG11GA-2012-321726) and a Distinguished Young Scientist award of the Turkish Academy of Sciences (TÜBA).

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    David P. Herzog

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

    Scott Hottovy

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

    Giovanni Volpe

  4. UNAM-Institute of Material Science and Nanotechnology, Bilkent University, 06800, Ankara, Turkey

    Giovanni Volpe

Authors
  1. David P. Herzog
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  2. Scott Hottovy
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  3. Giovanni Volpe
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Correspondence to Scott Hottovy.

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Herzog, D.P., Hottovy, S. & Volpe, G. The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction. J Stat Phys 163, 659–673 (2016). https://doi.org/10.1007/s10955-016-1498-8

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  • DOI: https://doi.org/10.1007/s10955-016-1498-8

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