论文标题
异常的动力学缩放决定了通用的临界奇点
Anomalous dynamical scaling determines universal critical singularities
论文作者
论文摘要
异常扩散现象发生在跨越细胞内到天体物理范围的长度尺度上。在重大位移的概率密度函数（缩放函数）的大量论点中的一种特定形式的衰减形式被得出，并证明暗示着归一化累积发生器中的普遍奇异性。连续时间随机步行的确切计算提供了与二阶相变的奇异性有关的范式示例。在有偏见的情况下，缩放量仅限于在漂移方向上的位移，并且奇异性没有平衡类似物。
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived and shown to imply universal singularities in the normalized cumulant generator. Exact calculations for continuous time random walks provide paradigmatic examples connected with singularities of second order phase transitions. In the biased case scaling is restricted to displacements in the drift direction and singularities have no equilibrium analogue.
