A random flight process associated to a Lorentz gas with variable density in a gravitational field

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Burdzy, Krzysztof¹  Rizzolo, Douglas² 

[1] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

[2] Univ Delaware, Dept Math Sci, 501 Ewing Hall, Newark, DE 19716 USA

关键词: Lorentz model;    External field;    Invariance principles;   

DOI  :  10.1016/j.spa.2017.04.002

来源: Elsevier

【 摘 要 】

We investigate a random flight process approximation to a random scatterer Lorentz gas with variable scatterer density in a gravitational field. For power function densities we show how the parameters of the model determine recurrence or transience of the vertical component of the trajectory. Finally, our methods show that, with appropriate scaling of space, time and the density of obstacles, the trajectory of the particle converges to a diffusion with explicitly given parameters. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free