Multi-point Distribution Function for the Continuous Time Random Walk

Details Multi-point Distribution Function for the Continuous Time Random Walk Multi-point Distribution Function for the Continuous Time Random Walk

2007-05-20

arxiv.org/abs/0705.2857v1

J. of Stat. Mech: Theory and Experiment P08001 (2007)

Physics

Condensed Matter

Statistical Mechanics

7 pages

Scientific paper

10.1088/1742-5468/2007/08/P08001

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 single point 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 aging CTRW single point distribution functions. The correlation function $$ for the biased CTRW process is found. The random walk foundation of the multi-time-space fractional diffusion equation [Baule and Friedrich [{\em Europhysics Letters} {\bf 77} 10002 (2007)] is investigated using the unbiased CTRW in the continuum limit.

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