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On the Distribution of Free Path Lengths¶for the Periodic Lorentz Gas

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Abstract:

Consider the domain

and let the free path length be defined as

The distribution of values of is studied in the limit as for all . It is shown that the value is critical for this problem: in other words, the limiting behavior of depends only on whether γ is larger or smaller than .

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Authors and Affiliations

  1. Institute for Advanced Study, School of Mathematics, Princeton NJ 08540, USA, , , , , , US

    Jean Bourgain

  2. Université Paris VII & Ecole Normale Supérieure, D.M.I., 45 rue d'Ulm, 75005 Paris, France, , , , , , FR

    François Golse

  3. Chalmers University of Technology, Department of Mathematics, 41296 Göteborg, Sweden, , , , , , SE

    Bernt Wennberg

Authors
  1. Jean Bourgain
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  2. François Golse
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  3. Bernt Wennberg
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Received: 1 March 1996 / Accepted: 25 March 1997

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Bourgain, J., Golse, F. & Wennberg, B. On the Distribution of Free Path Lengths¶for the Periodic Lorentz Gas . Comm Math Phys 190, 491–508 (1998). https://doi.org/10.1007/s002200050249

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  • DOI: https://doi.org/10.1007/s002200050249

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