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

Journal article

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.

Authors: Hening, A; Rizzolo, D; Wayman, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Mathematical Society
• Journal: Transactions of the American Mathematical Society
• Volume: 3
• Pages: 27-62
• Publication date: 2016-03-24
• Acceptance date: 2016-03-04
• DOI: 10.1090/btran/11
• ISSN: 0002-9947
• Keywords: Random flight process; Diffusion approximation; Lorentz gas; Random evolution; Transport process; Continuous time random walk