6 papers · 1 filter
Wishart Matrices and Quantum Geometry: Foundations and Applications in Quantum Information
Noémie C. Combe
We present a unified framework for the study of Wishart matrices (W_p(n,Σ)), which generalize the chi-squared distribution to matrix-variate settings and model the covariance struc…
On Duality, Legendre Bundles and Deformations
N. C. Combe, P. G. Combe, H. K. Nencka
We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in informa…
Shape Theory via the Atiyah--Molino Reconstruction and Deformations
Noémie C. Combe, Hanna N. Nencka
Reconstruction problems lie at the very heart of both mathematics and science, posing the enigmatic challenge: \emph{How does one resurrect a hidden structure from the shards of in…
Exploring information geometry: Recent Advances and Connections to Topological Field Theory
Noémie C. Combe, Philippe G. Combe, Hanna K. Nencka
This introductory text arises from a lecture given in Göteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically inc…
On the geometry of Kähler--Frobenius manifolds and their classification
Noémie. C. Combe
The purpose of this article is to show that flat compact Kähler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field Th…
Learning on hexagonal structures and Monge-Ampère operators
Noémie C. Combe
Dually flat statistical manifolds provide a rich toolbox for investigations around the learning process. We prove that such manifolds are Monge-Ampère manifolds. Examples of such…