We exhibit the analog of the entropy map for multivariate Gaussian distributions on local fields. As in the real case, the image of this map lies in the supermodular cone and it determines the distribution of the valuation vector. In general, this map can be defined for non-archimedian valued fields whose valuation group is an additive subgroup of the real line, and it remains supermodular. We also explicitly compute the image of this map in dimension 3.

翻译：我们展示了本地域多变量高斯分布的星盘映射图的类比。 和真实的情况一样, 该映射的图像位于超模式锥体中, 它决定着估值矢量的分布 。 一般来说, 该映射可以被定义为非结构价值的域, 其估值组是真实线的相加子集, 并且仍然是超模式 。 我们还在维度 3 中明确计算此映射的图像 。