Scaling limit for stochastic models originated from Hamiltonian dynamics

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800068
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: The University of Tokyo (2015-2016); Keio University (2013-2014)
• Principal Investigator: SASADA Makiko 東京大学, 大学院数理科学研究科, 准教授 (00609042)
• Research Collaborator: Stefano Olla ; Cedric Bernardin ; Marielle Simon
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 流体力学極限 / ハミルトン系 / 非勾配型 / スペクトルギャップ

Outline of Final Research Achievements

This project aims to establish the scaling limit for microscopic stochastic models obtained as models of physical and social phenomena to obtain their macroscopic properties. In particular, we focus on stochastic models originated from Hamiltonian dynamics, which is one of the most fundamental dynamics in the classical physics. We succeed to derive rigorously a stochastic partial differential equation from a nonlinear Hamiltonian dynamic with stochastic noise as its macroscopic fluctuation of energy. Also, we study the case where the strength of the noise goes to 0 in the scaling limit and show that the macroscopic behavior depends on the speed of this convergence.

Free Research Field

大規模相互作用系の確率解析