A volume estimate for the set of stable lattices

TL;DR

This paper demonstrates that in high-dimensional spaces, the collection of stable lattices occupies nearly the entire measure within the space of unimodular lattices, highlighting their prevalence.

Contribution

It provides a quantitative measure showing the dominance of stable lattices in high dimensions, a new insight into lattice stability distribution.

Findings

Stable lattices form an almost full measure set in high dimensions.

The result applies to the space of unimodular lattices.

High-dimensional stability is more common than previously understood.

Abstract

We show that in high dimensions the set of stable lattices is almost of full measure in the space of unimodular lattices.