The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
By Jens Marklof, Andreas Strombergsson. 2007
180 citations recorded by the source corpus.
The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we investigate the Boltzmann-Grad limit, where the radius of each scatterer tends to zero, and prove the existence of a limiting distribution for the free path length of the periodic Lorentz gas. We also discuss related problems, such as the statistical distribution of directions of lattice points that are visible from a fixed position.
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c2d3951f60c70a45443745436cccdc6328fcf8da
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In Applied Mathematics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Fine-Scale Statistics for the Multidimensional Farey Sequence (2012, result): “The proof of a limit distribution for PQ(k,D,A) for Farey fractions is therefore a corollary of the results of [15].”
- A Poincar\'e section for horocycle flow on the space of lattices (2012, unknown): “For similar applications in the context of higher dimensional generalizations of Farey sequences we refer the reader to [30] and [29].”
- The two-point correlation function of the fractional parts of $\sqrt{n}$ is Poisson (2013, background): “6) The limiting point process characterised by the probabilities E(k, I) is the same as for the directions of affine lattice points with irrational shift [10, 1]; in the notation of [1], E(k, I) = E0(k, I) = E0,ξ(k, I) with ξ / ∈ Q(2).”