Related papers: Statistical Bergman geometry
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
An outstanding open question, which has attracted renewed attention following the pioneering work of Huang--Li--Treuer, is whether, for a given positive integer $m$, there exists a complex manifold whose Bergman metric is locally isometric…
The Bergman $p$-analytic content ($1\leq p<\infty $) of a planar domain $\Omega $ measures the $L^{p}(\Omega )$-distance between $\overline{z}$ and the Bergman space $A^{p}(\Omega )$ of holomorphic functions. It has a natural analogue in…
In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential…
We prove that the isoperimetric profile of a convex domain $\Omega$ with compact closure in a Riemannian manifold $(M^{n+1},g)$ satisfies a second order differential inequality which only depends on the dimension of the manifold and on a…
The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case of Riemannian geometry, we can define a distance in terms…
We give a new geometric interpretation of the Amari-Cencov $\alpha$-connections $\nabla^{(\alpha)}$ from information geometry: On the space of densities $\operatorname{Dens}_+(M)$, we show that there exist Riemannian metrics $G^\alpha$,…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
In information geometry, one of the basic problem is to study the geomet-ric properties of statistical manifold. In this paper, we study the geometricstructure of the generalized normal distribution manifold and show that it has constant…
Let $D, \Omega_1, ..., \Omega_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $\Omega_1 \times... \Omega_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
In problems of parameter estimation from sensor data, the Fisher Information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the…
Information geometry is an important tool to study statistical models. There are some important examples in statistical models which are regarded as warped products. In this paper, we study information geometry of warped products. We…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and…
Comparing Neumann and Dirichlet eigenvalues of the Laplacian on a bounded domain $\Omega\subseteq\Rbb^n$ is a topic that goes back at least to the work of P\'olya \cite{polya}. We study the effect of the isoperimetric ratio of $\Omega$ on…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
Let $\Omega\subset\mathbb{C}^n$ be a bounded domain with smooth boundary, whose Bergman projection $B$ maps the Sobolev space $H^{k_{1}}(\Omega)$ (continuously) into $H^{k_{2}}(\Omega)$. We establish two smoothing results: (i) the full…
Let $\Omega$ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $\hbox{Reg}(\Omega)$ is K\"ahler-Einstein.