Invariant metric under deformed Markov embeddings with overlapped supports

2019/10/27 by Hiroshi Matsuzoe, Matsuzoe, Hiroshi, Asuka Takatsu +1
Mathematics · #53B12 #62B05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1910.12226

openalex publication_date 2019/10/27 · openalex created_date 2019/11/01 · openalex updated_date 2026/07/28

Abstract

Due to Čencov's theorem, there exists a unique family of invariant symmetric (0,2)-tensor fields on the space of positive probability measures on a set of n-points indexed by n∈ ℕ under Markov embeddings. We deform Markov embeddings keeping sufficiency, and prove existence and uniqueness of invariant families under the embeddings.

Citations

• An extended Čencov characterization of the information metric

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