Generalizations of Banaszczyk's Transference Theorems and Tail Bound. Miller, S. D. & Stephens-Davidowitz, N. 2018. Paper abstract bibtex 1 download We generalize Banaszczyk's seminal tail bound for the Gaussian mass of a lattice to a wide class of test functions. We therefore obtain quite general transference bounds, as well as bounds on the number of lattice points contained in certain bodies. As example applications, we bound the lattice kissing number in $\ell_p$ norms by $e^{(n+ o(n))/p}$ for $0 < p ≤ 2$, and also give a proof of a new transference bound in the $\ell_1$ norm.

@unpublished{MSGeneralizationsBanaszczyk18,
title = {Generalizations of {{Banaszczyk}}'s Transference Theorems and Tail Bound},
abstract = {We generalize Banaszczyk's seminal tail bound for the Gaussian mass of a lattice to a wide class of test functions. We therefore obtain quite general transference bounds, as well as bounds on the number of lattice points contained in certain bodies. As example applications, we bound the lattice kissing number in $\ell_p$ norms by $e^{(n+ o(n))/p}$ for $0 < p \leq 2$, and also give a proof of a new transference bound in the $\ell_1$ norm.},
url = {http://arxiv.org/abs/1802.05708},
author = {Miller, Stephen D. and {Stephens-Davidowitz}, Noah},
year = {2018}
}

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