arXiv subjects

Minoru W. Yoshida

Publications and source records attributed to Minoru W. Yoshida.

5 recordsLinked to original sources

arXiv2026

Homogenization of diffusions on the lattice ${\mathbf Z}^d$ with periodic drift coefficients; Application of logarithmic Sobolev inequality

A homogenization problem of infinite dimensional diffusion processes indexed by ${\mathbf Z}^d$ having periodic drift coefficients is considered. By an application of the uniform ergodic theorem for infinite dimensional diffusion processes based on logarithmic Sobolev inequalities, an homogenization property of the processes starting from an almost every arbitrary point in the state space with respect to an invariant measure is proved. This result is also interpreted as solution to a homogenization problem of infinite dimensional diffusions with random coefficients, which is essentially analogous to the known ones in finite dimensions.

math.PR↗

arXiv2026

Direct construction of scalar quantum fields by L{é}vy fields -- nontrivial exact Wightman fields in a wider field with a relaxed Gårding-Wightman Axioms-

This paper introduces partial results, in the current situation, of ongoing considerations corresponding to the above title. A construction on exact relativistic quantum field model with the space time dimension $d \in {\mathbb N}$, including the case where $d \geq 4$, is going to be discussed. Firstly, Hermitian scalar quantum fields $<{\cal H}, U, ψ, D>$, within a relaxed framework of the Gårding-Wightman Axioms, is constructed by making use of the stochastic calculus arguments with respect to the {\it{stationary additive random fields }} on ${\mathbb R}^d$, i.e., the {\it{L{é}vy random fields}} on ${\mathbb R}^d$. The first constructed $<{\cal H}, U, ψ, D>$, here, satisfy all the requirements of the the Gårding-Wightman Axioms, except that the field operators $ψ(f)$ with $f \in {\cal S}({\mathbb R}^d \to {\mathbb R})$ are symmetric operators on the physical Hilbert space ${\cal H}$, which situation is denoted here as {\it{a relaxed framework}} of the Gårding-Wightman Axioms. Secondly, by taking the adequate subspaces of ${\cal H}$, non trivial exact Wightman quantum fields, which satisfy all the requirements of the Gårding-Wightman Axioms, are constructed actually. keywords: Axiomatic quantum field theory, Gårding-Wightman axioms, Bochner-Minlos theorem, L{é}vy fields on ${\mathbb R}^d$.

math-ph↗

arXiv2023

A general formulation of Non-Local Dirichlet forms on infinite dimensional topological vector spaces and its applications, and corresponding subjects: Seminar at Univ. Lisboa,2023

A concise explanations on the results given by Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I, CMP 2021, by Sergio Albeverio, Minoru W. Yoshida, et.al., and Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces Part 2, Potential Analysis 2022, by Sergio Albeverio, Minoru W. Yoshida, et.al.are given as a digestive fashion.

math.FA↗

arXiv2021

Non-local Markovian symmetric forms on infinite dimensional spaces

General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $(S, {\cal B}(S), μ)$, with $S$ Fr{é}chet spaces such that $S \subset {\mathbb R}^{\mathbb N}$, ${\cal B}(S)$ is the Borel $σ$-field of $S$, and $μ$ is a Borel probability measure on $S$, are introduced. Firstly, a family of non-local Markovian symmetric forms ${\cal E}_{(α)}$, $0 < α< 2$, acting in each given $L^2(S; μ)$ is defined, the index $α$ characterizing the order of the non-locality. Then, it is shown that all the forms ${\cal E}_{(α)}$ defined on $\bigcup_{n \in {\mathbb N}} C^{\infty}_0({\mathbb R}^n)$ are closable in $L^2(S;μ)$. Moreover, sufficient conditions under which the closure of the closable forms, that are Dirichlet forms, become strictly quasi-regular, are given. Finally, an existence theorem for Hunt processes properly associated to the Dirichlet forms is given. The application of the above theorems to the problem of stochastic quantizations of Euclidean $Φ^4_d$ fields, for $d =2, 3$, by means of these Hunt processes is indicated.

math.PR↗

arXiv2021

Non-local Markovian symmetric forms on infinite dimensional spaces; Part 2. Examples: non local stochastic quantization of space cut-off quantum fields and infinite particle systems

The general framework on the non-local Markovian symmetric forms on weighted $l^p$ $(p \in [1, \infty])$ spaces constructed by [A,Kagawa,Yahagi,Y 2020], by restricting the situation where $p =2$, is applied to such measure spaces as the space cut-off $P(ϕ)_2$ Euclidean quantum field, the $2$-dimensional Euclidean quantum fields with exponential and trigonometric potentials, and the field describing a system of an infinite number of classical particles. For each measure space, the Markov process corresponding to the {\it{non-local}} type stochastic quantization is constructed.

math-ph↗