Lattice Gaussians maximize Shannon entropy, forming an exponential family tied to Riemann theta functions
FrnkNlsn · x · 2026-09-24
Frank Nielsen summarizes information-theoretic properties of lattice Gaussian distributions:
- Key result: Discrete lattice Gaussians maximize Shannon entropy and therefore form a discrete exponential family (DEF) whose cumulant function relates to the Riemann theta function.
- Literature: Includes the 2022 journal paper The Kullback–Leibler Divergence Between Lattice Gaussian Distributions (Journal of the Indian Institute of Science), a working paper on KL divergence between discrete normals, plus slides.
- Resources: His homepage aggregates papers, slides, and links on lattice Gaussians and statistical divergences.
Relevant to discretized probabilistic modeling, quantization, and lattice-based cryptography.
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