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The stochastic acceleration problem in two dimensions

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Abstract

We consider the motion of a particle in a two-dimensional spatially homogeneous mixing potential and show that its momentum converges to the Brownian motion on a circle. This complements the limit theorem of Kesten and Papanicolaou (1980) proved in dimensionsd≥3.

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Authors and Affiliations

  1. Institute of Mathematics, UMCS, pl. Marii Curie Skłodowskiej 1, 20-031, Lublin, Poland

    Tomasz Komorowski

  2. Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA

    Lenya Ryzhik

Authors
  1. Tomasz Komorowski
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  2. Lenya Ryzhik
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Komorowski, T., Ryzhik, L. The stochastic acceleration problem in two dimensions. Isr. J. Math. 155, 157–203 (2006). https://doi.org/10.1007/BF02773954

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  • DOI: https://doi.org/10.1007/BF02773954

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