论文标题
连续时间随机步行在幂律重置下
Continuous time random walks under power-law resetting
论文作者
论文摘要
我们研究了连续的时间随机步行（CTRW），其中包括重置等待时间的功率定律分布，这将步行者带回了起点，并在重置事件之间进行幂律分布。考虑了两种情况。在完整的重置下，重置事件重新开始后的CTRW具有新的等待时间，独立于史前史。在不完整的重置下，坐标的重置不会影响等待时间，直到下一次跳跃。我们关注步行者的平均平方位移（MSD）的行为，从其初始位置，在沃克位移的概率密度函数下显示普遍行为以及这种普遍行为本身的条件。我们表明，MSD的行为与缩放的布朗运动（SBM）相同，是CTRW的平均场模型。在完整重置（如果存在）下，CTRW的概率密度函数（PDF）的中间渐近学也与SBM的相应情况相同。但是，对于不完整的重置，CTRW和SBM的PDF的行为大不相同。
We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are considered. Under complete resetting, the CTRW after the resetting event starts anew, with a new waiting time, independent of the prehistory. Under incomplete resetting, the resetting of the coordinate does not influence the waiting time until the next jump. We focus on the behavior of the mean squared displacement (MSD) of the walker from its initial position, on the conditions under which the probability density functions of the walker's displacement show universal behavior, and on this universal behavior itself. We show, that the behavior of the MSD is the same as in the scaled Brownian motion (SBM), being the mean field model of the CTRW. The intermediate asymptotics of the probability density functions (PDF) for CTRW under complete resetting (provided they exist) are also the same as in the corresponding case for SBM. For incomplete resetting, however, the behavior of the PDF for CTRW and SBM is vastly different.
