Multi-point distribution function for the continuous time random walk

被引：28

作者：

Barkai, E. ^{[1
]}

Sokolov, I. M.

机构：

[1] Bar Ilan Univ, Dept Phys, IL-52900 Ramat Gan, Israel

[2] Humboldt Univ, Inst Phys, D-12489 Berlin, Germany

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2007年

关键词：

stochastic particle dynamics (theory); slow dynamics and ageing (theory); nonequilibrium. fluctuations in small systems; probability theory;

D O I：

10.1088/1742-5468/2007/08/P08001

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We derive an explicit expression for the Fourier - Laplace transform of the two- point distribution function p( x(1), t(1); x(2), t(2)) of a continuous time random walk ( CTRW), thus generalizing the result of Montroll and Weiss for the singlepoint distribution function p( x(1), t(1)). The multi- point distribution function has a structure of a convolution of the Montroll - Weiss CTRW and the ageing CTRW single- point distribution functions. The correlation function x( t(1)) x( t(2)) for the biased CTRW process is found. The random walk foundation of the multi- time space fractional diffusion equation is investigated using the unbiased CTRW in the continuum limit.

引用

页数：11

共 27 条

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