On the distribution of angles between increasingly many short lattice vectors
Artikel i vetenskaplig tidskrift, 2022

Following Södergren, we consider a collection of random variables on the space Xn of unimodular lattices in dimension n: normalizations of the angles between the N=N(n) shortest vectors in a random unimodular lattice, and the volumes of spheres with radii equal to the lengths of these vectors. We investigate the expected values of certain functions (whose support depends on a parameter K=K(n)) evaluated at these random variables in the regime where K and N are allowed to tend to infinity with n at the rate KN=o(n1/6). Our main result is that as n⟶∞, these random variables exhibit a joint Poissonian and Gaussian behavior.

Poisson process

Space of lattices

Rogers' integration formula

Författare

Kristian Holm

Chalmers, Matematiska vetenskaper, Algebra och geometri

Journal of Number Theory

0022-314X (ISSN) 1096-1658 (eISSN)

Vol. In Press

Ämneskategorier

Tillämpad psykologi

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1016/j.jnt.2022.02.001

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Senast uppdaterat

2022-04-20