Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spherical equidistribution in adelic lattices and applications   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.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci