Discrete Gaussian distributions via theta functions
Algebraic Geometry
2019-04-19 v2 Probability
Statistics Theory
Statistics Theory
Abstract
We study a discrete analogue of the classical multivariate Gaussian distribution. It is supported on the integer lattice and is parametrized by the Riemann theta function. Over the reals, the discrete Gaussian is characterized by the property of maximizing entropy, just as its continuous counterpart. We capitalize on the theta function representation to derive statistical properties. Throughout, we exhibit strong connections to the study of abelian varieties in algebraic geometry.
Cite
@article{arxiv.1801.02373,
title = {Discrete Gaussian distributions via theta functions},
author = {Daniele Agostini and Carlos Améndola},
journal= {arXiv preprint arXiv:1801.02373},
year = {2019}
}
Comments
23 pages. Final version. To appear in SIAGA. v2: changed notation and added references