Multi-point distribution function for the continuous time random walk

E. Barkai, IM Sokolov

Research output: Contribution to journalArticlepeer-review


We derive an explicit expression for the Fourier–Laplace transform of the two-point distribution function p(x1, t1; x2, t2) of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single-point distribution function p(x1, t1). 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 \langle x(t_1) x(t_2) \rangle 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.
Original languageAmerican English
JournalJournal of Statistical Mechanics: Theory and Experiment
StatePublished - 2007


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