The Boltzmann-Grad limit of the periodic Lorentz gas

• 成果类型: Article
• 署名作者: Marklof, Jens; Strombergsson, Andreas
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.1.7
• 发表日期: 2011
• 页码: 225-298
• 关键词: free-path lengths; sure invariance-principle; small-scatterer limit; STATISTICAL PROPERTIES; infinite-horizon; recurrence; systems

摘要

We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.