Lagrangian Submanifolds of Symplectic Structures Induced by Divergence Functions

Entropy

Marco Favretti¹ 

[1] Dipartimento di Matematica Tullio Levi-Civita, Università degli Studi di Padova, 35121 Padova, Italy;

关键词: canonical divergence;    Lagrangian submanifolds;    Morse family;    constrained optimization;    geometric phase transitions;   

DOI  :  10.3390/e22090983

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown