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arXiv · 1710.07944

Spherical equidistribution in adelic lattices and applications

Daniel El-Baz
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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.

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Daniel El-Baz. 2017-10-22. Spherical equidistribution in adelic lattices and applications. https://arxiv.org/abs/1710.07944

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