  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.
