McKeague Ian W
Department of Biostatistics, Columbia University.
Stat Probab Lett. 2015 Apr 1;99:149-155. doi: 10.1016/j.spl.2014.12.028.
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
已经提出了麦克斯韦-玻尔兹曼分布的几种相对论扩展，但它们无法解释各种天体物理源通量分布中观测到的对数正态尾部行为。受此问题的启发，在狭义相对论条件下发展了经典中心极限定理的扩展。结果与韦恩、斯特罗克和瓦拉丹发展的局部紧致李群上的中心极限定理有关，但在这种特殊情况下，渐近分布具有明确的形式，很容易看出它表现出对数正态尾部行为。
