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摘要翻译：
本文导出了连续时间随机游动(CTRW)的两点分布函数$P(x_1,t_1；x_2,t_2)$的Fourier-Laplace变换的显式表达式，从而推广了Montroll和Weiss对单点分布函数$P(x_1,t_1)$的结果。多点分布函数具有Montroll-Weiss CTRW和aging CTRW单点分布函数的卷积结构。发现了有偏CTRW过程的相关函数$<x(t_1)x(t_2)>$。利用连续极限下的无偏CTRW研究了多时空分数阶扩散方程[Baule和Friedrich[{em Europhysics Letters}{bf 77}10002(2007)]的随机游动基础。
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英文标题：
《Multi-point Distribution Function for the Continuous Time Random Walk》
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作者：
E. Barkai, I.M. Sokolov
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
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 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 $<x(t_1) x(t_2) >$ for the biased CTRW process is found. The random walk foundation of the multi-time-space fractional diffusion equation [Baule and Friedrich [{\em Europhysics Letters} {\bf 77} 10002 (2007)] is investigated using the unbiased CTRW in the continuum limit.
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PDF链接：
https://arxiv.org/pdf/705.2857
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