Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Combe, Noémie"'
Autor:
Combe, Noémie C.
We consider the cone of concentration matrices related to linear concentration models and Wishart laws. We prove that this cone is a Monge--Amp\`ere domain and that the log-likelihood function generates its potential function at the identity. The tan
Externí odkaz:
http://arxiv.org/abs/2501.01345
Autor:
Combe, Noemie C.
An important object appearing in the framework of the Tomita--Takesaki theory is an invariant cone under the modular automorphism group of von Neumann algebras. As a result of the connection between von Neumann algebras and quantum field theory, von
Externí odkaz:
http://arxiv.org/abs/2412.12289
Autor:
Combe, Noémie C.
Dually flat statistical manifolds provide a rich toolbox for investigations around the learning process. We prove that such manifolds are Monge-Amp\`ere manifolds. Examples of such manifolds include the space of exponential probability distributions
Externí odkaz:
http://arxiv.org/abs/2412.04407
Autor:
Combe, Noémie. C.
The purpose of this article is to show that flat compact K\"ahler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field Theory and closely related to Joyce structure. As a result, we classify
Externí odkaz:
http://arxiv.org/abs/2411.14362
Autor:
Combe, Noémie C.
Kontsevich suggested that the Landau-Ginzburg model presents a good formalism for homological mirror symmetry. In this paper we propose to investigate the LG theory from the viewpoint of Koopman-von Neumann's construction. New advances are thus provi
Externí odkaz:
http://arxiv.org/abs/2409.00835
Autor:
Combe, Noemie C.
We prove that in any strictly convex symmetric cone $\Omega$ there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra (with a res
Externí odkaz:
http://arxiv.org/abs/2309.04334
We prove that the information geometry's Frobenius manifold is a symplectic manifold having Poisson structures. By proving this statement, a bridge is created between the theories developed by Vinberg, Souriau and Koszul and the Frobenius manifold ap
Externí odkaz:
http://arxiv.org/abs/2201.07517
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more sophistic
Externí odkaz:
http://arxiv.org/abs/2112.15237
Autor:
Combe, Noemie C.
New relations between algebraic geometry, information theory and Topological Field Theory are developed. One considers models of databases subject to noise i.e. probability distributions on finite sets, related to exponential families. We prove expli
Externí odkaz:
http://arxiv.org/abs/2110.02607
Publikováno v:
Geometric Science of Information, 2021
In this paper, we explicitly prove that statistical manifolds, related to exponential families and with flat structure connection have a Frobenius manifold structure. This latter object, at the interplay of beautiful interactions between topology and
Externí odkaz:
http://arxiv.org/abs/2107.08446