Lagrangian Submanifolds of Symplectic Structures Induced by Divergence Functions
Lagrangian Submanifolds of Symplectic Structures Induced by Divergence Functions
Abstract
Divergence functions play a relevant role in Information Geometry as they allow for the introduction of a Riemannian metric and a dual connection structure on a finite dimensional manifold of probability distributions. They also allow to define, in a canonical way, a symplectic structure on the square of the above manifold of probability distributions, a property that has received less attention in the literature until recent contributions. In this paper, we hint at a possible application: we study Lagrangian submanifolds of this symplectic structure and show that they are useful for describing the manifold of solutions of the Maximum Entropy principle. View Full-Text
Keywords: canonical divergence; Lagrangian submanifolds; Morse family; constrained optimization; geometric phase transitions
Full Paper can be downloaded at: https://www.mdpi.com/1099-4300/22/9/983
This article belongs to the Special Issue Information Geometry III
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