TITLE OF PROJECT : SELFDIFFUSION MATRIX OF INTERACTING BROWNIAN MOTIONS
Project/Area Number  09640244 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  NAGOYA UNIVERSITY 
Principal Investigator 
OSADA Hirofumi NAGOYA UNIVERSITY,MATHEMATICS PROFESSOR, 大学院・多元数理科学研究科, 教授 (20177207)

CoInvestigator(Kenkyūbuntansha) 
FUNAKI Tadahisa TOKYO UNIVERSITY,MATHEMATICAL SCIENCE PROFESSOR, 大学院・数理科学研究科, 教授 (60112174)
KUSUOKA Shigeo TOKYO UNIVERSITY,MATHEMATICAL SCIENCE PROFESSOR, 大学院・数理科学研究科, 教授 (00114463)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  SELF=DIFFUSION COEFFICIENTS / INFINITE PARTICLE SYSTEM / INTERACTING BROWNIAN MOTION / HYDRODYNAMICAL LIMIT / 自己拡散係数 / 無限粒子系 / Interacting Brownian motion / 流体力学極限 
Research Abstract 
We completed and published the paper that says the selfdiffusion coefficient is positive for particles with convex hard cores in a multidimensional space, even if the density of the particle is very high. In order to prove this we use the variational formula of the selfdiffusion coefficient and a fine estimate of Gibbs measures derived from a result on oriented site percolation. Interacting Brownian motion is a dynamics of the motion of infinite amount of Brownian particles with interaction. To construct such a dynamics has some difficulty because this is indeed a problem to construct infinitely dimensional diffusion. For this we have solved the problem and publised the paper under very mild assumption such as the coefficients are measurable functions. So far the results are known only the restrict assumption such that the coefficients are upper semicontinuous. We improve this in such a way that they are bounded from both of below and above by upper semicontinuous functions. We think this generalization is quite satisfactory. We prove the positivity of the capacity of the existence of two particles at the same position is necessary for the positivity of the one dimensional selfdiffusion coefficient. Althogh we tried to prove this is also sufficient, it is in vain. While doing this research, we come to the new thema such that the same problem in the infinite volume path space. It is related to Log Sobolev inequality ; so I am now think this new problem is exciting.

Report
(4results)
Research Output
(14results)