TL;DR
This paper investigates the likelihood of large holes in random affine unimodular lattices and flat tori spectra, providing probabilistic bounds and discussing broader implications and open questions.
Contribution
It introduces bounds on the probability of large holes in random affine lattices and flat tori spectra, expanding understanding of their geometric properties.
Findings
Bound on probability of large holes in affine unimodular lattices
Bound on probability of large spectral holes in flat tori
Discussion of motivations, generalizations, and open questions
Abstract
We give a bound on the probability that a randomly chosen affine unimodular lattice has large holes, and a similar bound on the probability of large holes in the spectrum of a random flat torus. We discuss various motivations and generalizations, and state several open questions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics