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Masanori Hino

Publications and source records attributed to Masanori Hino.

At least 19 recordsLinked to original sources
arXiv2026

Limit Theorems for Persistent Homology of Multiparameter Complex Processes

Multiparameter complex processes, based on the Costa-Farber model, provide a common framework for growing random simplicial complexes, including the Linial-Meshulam and random flag complex processes. We establish laws of large numbers for persistent Betti numbers of these processes and prove that, after a deterministic time change and normalization, their persistence diagrams converge weakly in probability to a deterministic finite measure. Its quadrant masses are determined by universal limits of normalized persistent Betti numbers, characterized by an explicit finite-dimensional optimization problem. We extend the diagram convergence to integrals of continuous functions with polynomial growth in the death coordinate and controlled singularities at the diagonal. These results yield convergence of additive and multiplicative lifetime measures and total persistence. We further deduce convergence in optimal transport distance. The proofs combine local weak convergence of simplicial pairs, spectral analysis of compressed Laplacians accounting for dependence through shared faces, and quantitative estimates for large death coordinates and short lifetimes.

math.PR↗
arXiv2026

Pointwise regularity and irregularity of energy densities on $N$-dimensional Sierpinski gaskets

We study the pointwise regularity of energy densities associated with harmonic functions on the $N$-dimensional Sierpinski gasket $(N\ge 2)$ with respect to the Kusuoka measure. For any nonconstant harmonic function, we prove that every Borel representative of the density is discontinuous at every point of a set of full Kusuoka measure. In sharp contrast, on each one-dimensional edge of the gasket -- itself a set of zero Kusuoka measure -- the density admits a canonical pointwise version, which is $γ_N$-Hölder continuous on that edge with the explicit and optimal exponent $γ_N=\log_2 \{(\sqrt{4N+5}+1)/(\sqrt{4N+5}-1)\}$.

math.AP↗
arXiv2026

Fractional binomial distributions induced by the generalized binomial theorem and their applications

We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42} (2010), 467--477]). This provides a new probabilistic structure not representable as the law of the sum of independent and identically distributed random variables. Despite this nonstandard nature, we establish several of its fundamental analytic and probabilistic properties, including limit theorems,through a unified framework based on the generalized binomial theorem.We further analyze the properties of the fractional Bernstein operator associated with the fractional binomial distribution. In particular, we prove that the iterates of the operator converge to a generalized Wright--Fisher diffusion semigroup after a proper diffusive rescaling.

math.PR↗
arXiv2025

Martingale dimensions for a class of metric measure spaces

We establish a general analytic framework for determining the AF-martingale dimension of diffusion processes associated with strongly local regular Dirichlet forms on metric measure spaces. While previous approaches typically relied on self-similarity, our argument is based instead on purely analytic balance conditions between energy measures and relative capacities. Under this localized analytic condition, we prove that the AF-martingale dimension collapses to one, thereby indicating that the intrinsic stochastic structure remains effectively one-dimensional even on highly irregular or inhomogeneous spaces. As a key technical ingredient, our proof employs a simultaneous blow-up and push-forward scheme for harmonic functions and their energy measures, allowing us to control the limiting behavior across scales without invoking heat kernel bounds or explicit geometric models. The main theorem is applied in particular to inhomogeneous Sierpinski gaskets, which do not possess self-similarity or uniform geometric structure. Our method provides a general analytic perspective that can be used to study the one-dimensional probabilistic structure of diffusions through martingale additive functionals.

math.PR↗
arXiv2025

Asymptotic behaviors of fractional binomial distributions derived from the generalized binomial theorem

A fractional binomial distribution, introduced by Hino and Namba (2024) via the generalized binomial theorem, is a fractional variant of the classical binomial distribution. Building upon previous work that established limit theorems, such as the weak law of large numbers and the central limit theorem, for fractional binomial distributions, this paper further investigates their asymptotic behaviors. Specifically, we derive the large and moderate deviation principles and a Berry--Esseen type estimate for these distributions.

math.PR↗
arXiv2023

Estimates of the local spectral dimension of the Sierpinski gasket

We discuss quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski gasket. The present arguments were inspired by a previous study of the distribution of the Kusuoka measure by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpiński gasket, Indiana Univ. Math. J. 63 (2014), 831-868].

math.PR↗
arXiv2019

Asymptotic behavior of lifetime sums for random simplicial complex processes

We study the homological properties of random simplicial complexes. In particular, we obtain the asymptotic behavior of lifetime sums for a class of increasing random simplicial complexes; this result is a higher-dimensional counterpart of Frieze's $ζ(3)$-limit theorem for the Erdős-Rényi graph process. The main results include solutions to questions posed in an earlier study by Hiraoka and Shirai about the Linial-Meshulam complex process and the random clique complex process. One of the key elements of the arguments is a new upper bound on the Betti numbers of general simplicial complexes in terms of the number of small eigenvalues of Laplacians on links. This bound can be regarded as a quantitative version of the cohomology vanishing theorem.

math.PR↗
arXiv2016

An integrated version of Varadhan's asymptotics for lower-order perturbations of strong local Dirichlet forms

The studies of Ramírez, Hino-Ramírez, and Ariyoshi-Hino showed that an integrated version of Varadhan's asymptotics holds for Markovian semigroups associated with arbitrary strong local symmetric Dirichlet forms. In this paper, we consider non-symmetric bilinear forms that are the sum of strong local symmetric Dirichlet forms and lower-order perturbed terms. We give sufficient conditions for the associated semigroups to have asymptotics of the same type.

math.PR↗
arXiv2015

Some properties of energy measures on Sierpinski gasket type fractals

We confirm, in a more general framework, a part of the conjecture posed by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpiński gasket, Indiana Univ. Math. J. 63 (2014), 831--868] on the distribution of energy measures for the canonical Dirichlet form on the two-dimensional standard Sierpinski gasket.

math.PR↗
arXiv2013

Geodesic distances and intrinsic distances on some fractal sets

Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an analytic way, respectively, and they are closely related with each other in some classical situations. In this paper, we study the relations of these distances when the underlying space has a fractal structure. In particular, we prove their coincidence for a class of self-similar fractals.

math.PR↗
arXiv2012

Dirichlet spaces on H-convex sets in Wiener space

We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$. We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset if $U$ is $H$-convex and $H$-open. For the proof, the relations between $H$-notions and quasi-notions are also studied.

math.PR↗
arXiv2012

Measurable Riemannian structures associated with strong local Dirichlet forms

We introduce Riemannian-like structures associated with strong local Dirichlet forms on general state spaces. Such structures justify the principle that the pointwise index of the Dirichlet form represents the effective dimension of the virtual tangent space at each point. The concept of differentiations of functions is studied, and an application to stochastic analysis is presented.

math.PR↗
arXiv2012

Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.

math.PR↗
arXiv2010

Fractional order Taylor's series and the neo-classical inequality

We prove the neo-classical inequality with the optimal constant, which was conjectured by T. J. Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310]. For the proof, we introduce the fractional order Taylor's series with residual terms. Their application to a particular function provides an identity that deduces the optimal neo-classical inequality.

math.CA↗