Statistics of Gaussians on local fields and their tropicalizations

09/02/2019

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by   Yassine El Maazouz, et al.

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We study multivariate Gaussian distributions on local fields such as the field of p-adic numbers. We introduce the Bruhat-Tits building as a parameter space for Gaussian distributions and study some classic statistical problems in this setting. Finally we study geometric and probabilistic structures of the tropicalization of such distributions.