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

作者：Burdzy Krzysztof; Rizzolo Douglas^*

来源：Stochastic Processes and Their Applications, 2018, 128(1): 79-107.

DOI：10.1016/j.spa.2017.04.002

• Lorentz model
• External field
• Invariance principles

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.

• 出版日期2018-1