13 citations · 42 across the 10 of their papers we have counts for
12 papers
Moment polytopes of toric exponential families
Mathieu Molitor
We show that the moment polytope of a Kähler toric manifold, constructed as the torification (in the sense of M. Molitor, Kähler toric manifolds from dually flat spaces, arXiv:2109…
Geometric spectral theory for Kähler functions
Mathieu Molitor
We consider Kähler toric manifolds that are torifications of statistical manifolds in the sense of [M. Molitor, "Kähler toric manifolds from dually flat spaces",…
Weyl group of the group of holomorphic isometries of a Kähler toric manifold
Mathieu Molitor
We compute the Weyl group (in the sense of Segal) of the group of holomorphic isometries of a Kähler toric manifold with real analytic Kähler metric.
Kahler toric manifolds from dually flat spaces
Mathieu Molitor
We present a correspondence between real analytic Kähler toric manifolds and dually flat spaces, similar to Delzant correspondence in symplectic geometry. This correspondence gives…
One-dimensional exponential families with constant Hessian scalar curvature
Mathieu Molitor
We give a complete classification of 1-dimensional exponential families defined over a finite space whose Hessian scalar curvature is constan…
Gaussian distributions, Jacobi group and Siegel-Jacobi space
Mathieu Molitor
Let be the space of Gaussian distribution functions over , regarded as a 2-dimensional statistical manifold parameterized by the mean and the deviatio…
Generalization of Hasimoto's transformation
Mathieu Molitor
In this paper, we generalize the famous Hasimoto's transformation by showing that the dynamics of a closed unidimensional vortex filament embedded in a three-dimensional manifold o…
The group of unimodular automorphisms of a principal bundle and the Euler-Yang-Mills equations
Mathieu Molitor
Given a principal bundle G \rightarrow P \rightarrow B (each being compact, connected and oriented) and a G-invariant metric h^{P} on P which induces a volume form μ^{P}, we consid…
Remarks on the space of volume preserving embeddings
Mathieu Molitor
Let (N,g) be a Riemannian manifold. For a compact, connected and oriented submanifold M of N. we define the space of volume preserving embeddings Emb_μ(M,N) as the set of smooth em…
Information geometry and the hydrodynamical formulation of quantum mechanics
Mathieu Molitor
Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M. In this paper, we show that the Frechet mani…
Exponential families, Kahler geometry and quantum mechanics
Mathieu Molitor
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For…
Remarks on the statistical origin of the geometrical formulation of quantum mechanics
Mathieu Molitor
A quantum system can be entirely described by the Kähler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometri…