What type of study is this?

This is a Quantitative Study study.

September 29, 2025Open Access

Limit distributions for SO (n, 1) action on k-lattices in R^n+1

Puntos clave

The measures converge to a semi-invariant probability measure supported on orthogonal lattices.
Special 2-lattices in R^3 lie in hyperplanes tangent to the light cone and exhibit unique behavior.
The study resolves a conjecture by Sargent and Shapira as a case of the general result.
The analysis involves the asymptotic distribution of lattice actions on moduli space.

Resumen

We study the asymptotic distribution of norm ball averages along orbits of a lattice SO (n, 1) acting on the moduli space of pairs of orthogonal discrete subgroups of R^n+1 up to homothety. Our main result shows that, except for special 2-lattices in R³ lying in hyperplanes tangent to the light cone, these measures converge to an explicit semi-invariant probability measure supported on the space of homothety classes of pairs of orthogonal lattices tangent to the light cone. Our main motivation is a conjecture of Sargent and Shapira, which is resolved as a special case of our general result.

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Cite This Study

Bersudsky et al. (Sun,) studied this question.

synapsesocial.com/papers/68da5a3ec1728099cfd11961 https://doi.org/https://doi.org/10.48550/arxiv.2505.19413