2012 Fiscal Year Final Research Report

Deriving crystallizing probability model from classical mechanics

Research Project

Project/Area Number	21740063
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	University of Tsukuba
Principal Investigator	LIANG Song 筑波大学, 数理物質系, 准教授 (60324399)
Project Period (FY)	2009 – 2012
Keywords	確率論
Research Abstract	Put heavy particle(s) into an ideal gas environment, a system consists of infinitely many light particles with a certain initial distribution, and assume that the interactions between particles are non-random. We are interested in the problem of the limit behavior of the heavy particle(s) when the mass of the light particles converges to 0. When there are exact two heavy particles of different types, we proved that the distribution of the considered stochastic process converges to a diffusion with reflecting; for the case where the two heavy particles are of same type with relative efficiency, we found the concrete expression of the candidate limit process by proving the convergence of the corresponding stochastic differential equation. The similar problem with wave environment is also studied for the case with one heavy particle and in one-dimension.

(4 results)