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arXiv · 1906.02271

One-dimensional exponential families with constant Hessian scalar curvature

Mathieu Molitor
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Abstract

We give a complete classification of 1-dimensional exponential families $\mathcal{E}$ defined over a finite space $\Omega=\{x_{0}, ...,x_{n}\}$ whose Hessian scalar curvature is constant. We observe an interesting phenomenon: if $\mathcal{E}$ has constant Hessian scalar curvature, say $\lambda$, then $\lambda=\tfrac{2}{k}$ for some positive integer $k\leq m$. We also discuss the central role played by the binomial distribution in this classification.

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Mathieu Molitor. 2019-06-05. One-dimensional exponential families with constant Hessian scalar curvature. https://arxiv.org/abs/1906.02271

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