| Co-Investigator(Kenkyū-buntansha) |
SHIGA Tokuzo Tokyo Inst Tech, Grad.Sch.Sci.Eng., Professor, 大学院・理工学研究科, 教授 (60025418)
HIGUCHI Yasunari Kobe Univ., Fac.Sci., Professor, 理学部, 教授 (60112075)
OSADA Hirofumi Kyushu Univ., Grad.Sch.Math.Sci., Professor, 大学院・数理学研究院, 教授 (20177207)
TANEMURA Hideki Chiba Univ., Fac.Sci., Associate Professor, 理学部, 助教授 (40217162)
YOSHIDA Nobuo Kyoto Univ., Grad.Sch.Sci., Associate Professor, 大学院・理学研究科, 助教授 (40240303)
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| Research Abstract |
The large scale interacting systems generically mean mathematical models which are introduced to explain and understand physical phenomena at macroscopic level from microscopic one. Such systems exhibit very complicated feature in general. The purpose of this research is, unifying the viewpoints of stochastic analysis and theory of nonlinear partial differential equations, to study these models from several aspects deeply. To achieve the goal, in the first year 2002 of this research, an international symposium "Stochastic Analysis on Large Scale Interacting Systems" was organized. This played an important role to find the direction of the research.
The objects of the research were expansive and of wide range. Let us state some of them concretely : lattice interface model, derivation-of free boundary, problem, large deviation, quasi-Winterbottom shape, phase structure and phase separation curve in Widom-Rowlinson model, interacting Brownian particles, random matrices, parabolic Anderson model, polymers in random media, non-crossing random walks, epidemic model and phase coexistence, evolutional singular limit with pinning, combustion model and partial differential equation with singular term, two-phase obstacle model, stochastic partial differential equations with singular term like delta-functions, integration by parts formula for restricted Wiener measure, Wiener integrals for Bessel processes.
As research results based on effective cooperation of investigators in the group, we state : derivation of differential equations with singularities, like evolutionary variational inequality and free boundary problem, starting from interface model or two component system, finding similarity in interacting random walks or polymer models with interface model, study of interacting Brownian particles from several different aspects, studying the behavior of phase separation curves and others.
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