The geometric structures and instability of entropic dynamical models
type: Item
instance of: scholarly article
title: The geometric structures and instability of entropic dynamical models
zbMATH Open document ID: 1257.53024
author: Linyu Peng
author: Huafei Sun
author: Dandi Sun
author: Jin Yi
published in: Advances in Mathematics
publication date: 2011-04-20T00:00:00Z
review text: From the text: In this paper, we study two entropic dynamical (ED) models, 2D and 3D statistical manifolds \(\mathcal M_1\) and \(\mathcal M_2\) which serve as the stage on which the entropic dynamics evolves. The structure is obtained from the viewpoint of information geometry. Using the obtained Riemannian curvature tensor or Christoffel symbols we get the Jacobi vector field associated with the geodesic deviation equations on the manifolds, the asymptotic behavior of which conversely indicates the behavior of the geodesics. These are concluded for the two models, respectively as follows: first-order linearly divergent instability for ED1, and exponential instability for ED2. This progress is extremely special and important, based on that statistical curvature is used to characterize the chaos of a given entropic dynamical model, rather than only quantities on the associated manifolds.
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 62B10
zbMATH DE Number: 5880830
zbMATH Keywords: Jacobi field
zbMATH Keywords: information geometry
zbMATH Keywords: statistical manifold
zbMATH Keywords: scalar curvature
zbMATH Keywords: geodesic
MaRDI profile type: Publication
full work available at URL: j.aim.2011.02.002
OpenAlex ID: W2070208184
Wikidata QID: Q124890873
cites work: Differential-geometrical methods in statistics
cites work: Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections, and divergence
cites work: Q4527387
cites work: Jacobi fields on statistical manifolds of negative curvature
cites work: Q4003026
cites work: Spatial statistics and information geometry for parametric statistical models of galaxy clustering
cites work: Q4040875
cites work: The geometric structure of the inverse gamma distribution
DOI: 10.1016/J.AIM.2011.02.002
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description: scientific article; zbMATH DE number 5880830