PreprintCC BY 4.0arXiv
Void probabilities for perturbed lattices under mixing
Abstract
We study void probabilities for stationary perturbed lattices with possibly dependent perturbations. Our main result gives a general upper bound in terms of two ingredients: the number of lattice sites having a uniformly positive probability of hitting the observation set, and the α-mixing rate of the perturbation field. For unions of lattice cubes, this yields explicit bounds without moment or regularity assumptions on the marginal distribution of the perturbations. As a consequence, we obtain quantitative estimates for growing bounded Borel sets with non-empty interior, including stretched-exponential decay under exponential mixing and polynomial decay under polynomial mixing.
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BibTeX
@misc{flimmel2026void,
title = {{Void probabilities for perturbed lattices under mixing}},
author = {Daniela Flimmel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24650},
eprint = {2610.24650},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24650},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Void probabilities for perturbed lattices under mixing
AU - Daniela Flimmel
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24650
UR - https://arxiv.org/abs/2610.24650
AB - We study void probabilities for stationary perturbed lattices with possibly dependent perturbations. Our main result gives a general upper bound in terms of two ingredients: the number of lattice sites having a uniformly positive probability of hitting the observation set, and the α-mixing rate of the perturbation field. For unions of lattice cubes, this yields explicit bounds without moment or regularity assumptions on the marginal distribution of the perturbations. As a consequence, we obtain quantitative estimates for growing bounded Borel sets with non-empty interior, including stretched-exponential decay under exponential mixing and polynomial decay under polynomial mixing.
ER -