Markov invariant geometry and manifolds of states

DOI10.1007/BF01095975zbMath0734.60004OpenAlexW2088655718MaRDI QIDQ810989

E. A. Morozova, Nikolaj N. Chentsov

Publication date: 1991

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01095975

zbMATH Keywords

invariant linear connectionsinvariant metricsMarkov mapsRiemann-Christoffel curvature tensor

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) General considerations in statistical decision theory (62C05)

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Cites Work

• General state changes in quantum theory
• Defining the curvature of a statistical problem (with applications to second order efficiency)
• Differential-geometrical methods in statistics
• A new axiomatic approach in the theory of operator algebras
• Positive projections and Jordan structure in operator algebras.
• Equivariants in the category of Markov maps
• Statistical Isomorphism
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