Discrete Gaussian distributions via theta functions

01/08/2018

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by   Daniele Agostini, et al.

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We introduce a discrete analogue of the classical multivariate Gaussian distribution. It is parametrized by the Riemann theta function on the integer lattice. Our real-valued discrete Gaussian is characterized by the property of maximizing entropy, just as its continuous counterpart. We capitalize on the theta function representation to derive fundamental properties such as its characteristic function. Throughout, we exhibit strong connections to the study of abelian varieties in algebraic geometry.