The free path in a high velocity random flight process associated to a Lorentz gas in an external field
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- by Alexandru Hening, Douglas Rizzolo and Eric S. Wayman HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 3 (2016), 27-62
Abstract:
We investigate the asymptotic behavior of the free path of a variable density random flight model in an external field as the initial velocity of the particle goes to infinity. The random flight models we study arise naturally as the Boltzmann-Grad limit of a random Lorentz gas in the presence of an external field. By analyzing the time duration of the free path, we obtain exact forms for the asymptotic mean and variance of the free path in terms of the external field and the density of scatterers. As a consequence, we obtain a diffusion approximation for the joint process of the particle observed at reflection times and the amount of time spent in free flight.References
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Additional Information
- Alexandru Hening
- Affiliation: Department of Statistics, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, United Kingdom
- Email: hening@stats.ox.ac.uk
- Douglas Rizzolo
- Affiliation: Department of Mathematical Sciences, University of Delaware, 15 Orchard Road, Newark, Delaware 19716
- MR Author ID: 814330
- Email: drizzolo@udel.edu
- Eric S. Wayman
- Affiliation: Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, California 94720-3840
- MR Author ID: 1124479
- Email: ewayman@gmail.com
- Received by editor(s): March 8, 2015
- Published electronically: May 24, 2016
- Additional Notes: The first author was supported by EPSRC grant EP/K034316/1
The second author was supported by NSF grant DMS-1204840 - © Copyright 2016 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 3 (2016), 27-62
- MSC (2010): Primary 60F17; Secondary 60J60, 82C70
- DOI: https://doi.org/10.1090/btran/11
- MathSciNet review: 3503953