The Lorentz Gas with a Nearly Periodic Distribution of Scatterers

We consider the Lorentz gas in a distribution of scatterers which microscopically converges to a periodic distribution, and prove that the Lorentz gas in the low density limit satisfies a linear Boltzmann equation. This is in contrast with the periodic Lorentz gas, which does not satisfy the Boltzmann equation in the limit.

Automated summary

We study the Lorentz gas in a distribution of scatterers and find that it satisfies a linear Boltzmann equation in the low density limit, while the periodic Lorentz gas does not satisfy the Boltzmann equation in the limit.