Stochastic analytic study on Kardar-Parisi-Zhang equation

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610019
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Funaki Tadahisa 東京大学, 大学院数理科学研究科, 教授 (60112174)
• Co-Investigator(Renkei-kenkyūsha): MATANO HIROSHI 東京大学, 大学院数理科学研究科, 教授 (40126165) ; SASADA Makiko 東京大学, 大学院数理科学研究科, 准教授 (00609042) ; OSADA HIROFUMI 九州大学, 大学院数理学研究院, 教授 (20177207) ; KUMAGAI Takashi 京都大学, 数理解析研究所, 教授 (90234509) ; OTOBE YOSHIKI 信州大学, 理学部, 准教授 (30334882) ; XIE BIN 信州大学, 理学部, 准教授 (50510038)
• Research Collaborator: SPOHN Herbert ミュンヘン工科大学, 名誉教授 ; QUASTEL Jeremy トロント大学, 教授 ; WEBER Hendrik ウォーリック大学, 講師
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 確率論 / 解析学 / 統計力学 / 数理物理 / 関数方程式論

Outline of Final Research Achievements

Kardar-Parisi-Zhang (KPZ) equation is a nonlinear stochastic partial differential equation which describes an evolution of growing interfaces with fluctuation. Mathematically, this equation involves a divergent term so that it is ill-posed, but Hairer, a Fields medalist, introduced a method of renormalization which removes the divergent term and gave a mathematical meaning to it. In this research project, we have specified the stationary measures of KPZ equation and multicomponent coupled KPZ equation, and shown the global solvability in time. Moreover, we have found new determinantal structures in related interacting infinite particle systems.

Free Research Field

確率論