2016/03/09 by Jens Marklof, Marklof, Jens, Ilya Vinogradov +1
Mathematics · Physics and Astronomy · #37A17 #60B10 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #math-ph #math.DS #math.MP #math.PR #msc:37A17 #msc:60B10
paper · pdf · doi:10.48550/arxiv.1603.02779
arxiv created 2016/03/09 · openalex publication_date 2016/03/09 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A marked lattice is a d-dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on \mathbb Zd. We prove that, if the field is strongly mixing with a faster-than-logarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a non-trivial fiber bundle over such a space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the Boltzmann-Grad limit.