Probability & Statistics seminar: The free path in a high velocity random flight process associated to a Lorentz gas in an external field

20 November 2015, 3.40 PM - 20 November 2015, 4.40 PM

Alexandru Hening, Oxford

SM3, School of Mathematics

Alexandru Hening, University of Oxford

The free path in a high velocity random flight process associated to a Lorentz gas in an external field

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. This is based on joint work with Doug Rizzolo and Eric Wayman.

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Organisers: Marton Balazs, Haeran Cho

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