Spherical equidistribution in adelic lattices and applications

2017/10/22 by Daniel El-Baz, El-Baz, Daniel · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1710.07944

openalex publication_date 2017/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study spherical equidistribution on the space of (translates of) adelic lattices, which we apply to understand the fine-scale statistics of the directions in the set of shifted primitive lattice points. We also apply our results to the distribution of the free path lengths in the Boltzmann--Grad limit for point sets such as (possibly non-rational) translates of the lattice points all of whose coordinates are squarefree. Besides the equidistribution results for translates of expanding horospheres, a key ingredient is a probabilistic argument which allows us to tackle the technical difficulty of dealing with characteristic functions of compact sets with positive measure and empty interior.

Citations

• Uniform Distribution in Model Sets

Cited by

• Extreme events and impact statistics for unipotent actions on the space of lattices

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