Mathematical analysis system Laboratory

M. W. Yoshida

Minoru W. Yoshida
(Professor)

Office: 23-427 Ext.: 3734

e-mail:  ft101945kb@kanagawa-u.ac.jp

Engineering Ph.D., Osaka University

W. Kumagai

Wataru Kumagai
(Assistant Professor)

Laboratory: 23-426 Ext.:3733

e-mail:  kumagai@kanagawa-u.ac.jp

Information sciences Ph.D., Tohoku University

Research Field

Probability theory, Functional analysis, Mathematical physics, Mathematical sciences, Information mathematics, Artificial intelligence.

Research Overview

Stochastic analysis on infinite dimensional spaces, Random fields and their application to mathematical physics and mathematical sciences, Quantum information.

Research Subjects

    Stochastic partial differential equations, Constructive quantum field theory, Stochastic control, Quantum computer.

Introduction:

In this laboratory we perform researches on the problems of applied mathematics appearing in engineering, social sciences and natural sciences. The research methods adopted here are mathematics, substantially, but several information scientific techniques are also used efficiently.
Students in this laboratory shall study, for example, Markov decision theory and their applications, models of biological systems formulated by statistical mechanics, game theory and its applications and stochastic control. Not only these subjects, however, each one will be able to complete his or her research on each one’s individual interest of mathematical sciences.
To realize abstract or general mathematical (scientific) results by means of computer is also an important research subject in this laboratory. Precisely, the derivations of numerical concrete, or in some cases visual, results corresponding to some abstract mathematical statements by using computer are investigated. These experiences on researches performing in such manner (namely, through mathematics together with computer) give strong powers for students who will take active parts in the society.
Besides the above mentioned research subjects, in this laboratory we have been continuing the research on constructive (relativistic) quantum field theory which is a most important problem of mathematical physics and infinite dimensional analysis and is not solved completely for this 50 years. It is possible to say that to investigate and clarify this problem is to certify a consistency of the mathematical structure (equivalently, the way of cognition of all life).  

Publications

    M. W. Yoshida:

  • 1)“A homeomorphism relating path spaces of stochastic processes with values in respectively ,” Infinite Dimensional Analysis, Quantum Probability and Related Topics,Vol. 17,No. 1, pp. 219-257 (2014).
  • 2)“Some abstract considerations on the homogenization problem of infinite dimensional diffusions,” RIMS K ky roku,Bessatsu,B21,pp. 183-192 (2010).
  • 3)“Hida distribution construction of non-Gaussian reflection positive generalized random fields,” Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol.12, No. 1, pp. 21-49 (2009).
  • 4)“Systems of classical particles in the grand canonical ensemble, scaling limits and quantum field theory,” Review in Math. Phys. Vol.17, No. 2, pp. 176-226 (2005).
  • 5)“On the essential self-adjointness of Wick powers of relativistic fields and of fields unitary equivalent to random fields,” Acta Applicande Mathematicae, Vol. 80, No. 3, pp. 309-334 (2004).
  • 6)“H-C2 maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field,” J. Functional Analysis, Vol. 196, No. 2, pp.265-322 (2002).
  • 7)“Construction of infinite dimensional interacting diffusion processes through Dirichlet forms,” Probab. Theory Relat. Fields. Vol.106, No.2, pp. 265-297 (1996).

    W. Kumagai:

  • 1)“Entanglement Concentration is Irreducible,” Phys. Rev. Lett. 111(13), 130407 (2013).
  • 2)”Second Order Asymptotics for Random Number Generation,” 2013 IEEE Intern. Symp. on Inform. Theo. Proceedings, pp.1506-1510 (2013).
  • 3)“Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2 , t-, and F-Tests,” Comm. in Math. Phys, 318(2), pp.535-574 (2013).
  • 4)“A Characterization of Extended Monotone Metrics,” Linear Algebra and its Appl., 434(1), pp.224-231 (2011).
Current members
◯ Professors: 1 ◯ Assistant Professors: 1
◯ Postgraduates: 1 ◯ Undergraduates: 7

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