Greeting

Preface

This study aims at building the stochastic analytics of the infinite particle system based on the new theory of the infinite-dimensional stochastic differential equation with symmetry. This analytics is effective for the system to have the long-distance strong interaction that a hand was not able to start so far including the particle system to appear for broaching as a thermodynamic limit of the eigenvalue of the random matrices and zero points of the Gaussian analytic function and all Gibbs measures. We elucidate various novel phenomena that are different from the standard Gibbs measures because of the long-distance strong interaction.
About the exact solvable model such that the class of the infinite particle system in the one-dimensional space of reverse temperature β = 2 with the logarithm interference potential, we combine the structure with the stochastic analysis, and obtain explicit information about the solution of infinite-dimensional stochastic differential equations. Most for the study are related with random matrices and are related to the statistics physics such as the KPZ equation. With an expanse to cross over analysis / geometry / algebra as the single-mindedness mathematics including the class of various new point processes, stochastic partial differential equations, and stochastic geometry, we wrestle as a touchstone about the theoretical effectiveness by problems in mathematical physics.
This study elucidates the above-mentioned problem with Tadahisa Funaki (Waseda University), Hideki Tanemura (Chiba University), Makoto Katori (Chuo University), Takashi Kumagai (Res. Inst. for Mathematical Sci., Kyoto Univ.), Tomoyuki Shirai (Kyushu University, MI Institute), Tomohiro Sasamoto (Tokyo Institute of Technology) of the partakers.

On behalf of the research,
Hirofumi Osada (Kyushu University / Stochastic Analysis Research Center)