2012 Fiscal Year Final Research Report
Deriving crystallizing probability model from classical mechanics
| Project/Area Number |
21740063
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
LIANG Song 筑波大学, 数理物質系, 准教授 (60324399)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 確率論 |
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| 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.
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