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

Krzysztof Burdzy and Douglas Rizzolo

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 79-107

Abstract: 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.

Keywords: Lorentz model; External field; Invariance principles (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:1:p:79-107

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DOI: 10.1016/j.spa.2017.04.002

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