21 citations · 55 across the 32 of their papers we have counts for
8 papers · 1 filter
Divergence and Deformed Exponential Family
Hiroshi Matsuzoe, Asuka Takatsu
The Kullback--Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus…
Spectral convergence of high-dimensional spheres to Gaussian spaces
Asuka Takatsu
We prove that the spectral structure on the -dimensional standard sphere of radius compatible with a projection onto the first -coordinates converges to the spe…
Invariant metric under deformed Markov embeddings with overlapped supports
Hiroshi Matsuzoe, Asuka Takatsu
Due to Čencov's theorem, there exists a unique family of invariant symmetric -tensor fields on the space of positive probability measures on a set of -points indexed by $…
Equality in the logarithmic Sobolev inequality
Shin-ichi Ohta, Asuka Takatsu
We investigate the rigidity problem for the logarithmic Sobolev inequality on weighted Riemannian manifolds satisfying . Assuming equality holds, we…
Convergence of combinatorial Ricci flows to degenerate circle patterns
Asuka Takatsu
We investigate the combinatorial Ricci flow on a surface of nonpositive Euler characteristic when the necessary and sufficient condition for the convergence of the combinatorial Ri…
Displacement convexity of generalized relative entropies.II
Shin-ichi Ohta, Asuka Takatsu
We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler man…