Kumar Niraj, Harbola Upendra, Lindenberg Katja
Department of Chemistry and Biochemistry, BioCircuits Institute, University of California-San Diego, La Jolla, 92093-0340, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Aug;82(2 Pt 1):021101. doi: 10.1103/PhysRevE.82.021101. Epub 2010 Aug 2.
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, or superdiffusive behavior in different parameter regimes. This appears to be an instance of a single random walk model leading to all three forms of behavior by simply changing parameter values. Furthermore, the model offers the great advantage of analytical tractability. Our model is non-Markovian in that the next jump of the walker is (probabilistically) determined by the history of past jumps. It also has elements of intermittency in that one possibility at each step is that the walker does not move at all. This rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior.
我们提出了一个随机游走模型，该模型在不同的参数区域表现出渐近亚扩散、扩散或超扩散行为。这似乎是一个单一随机游走模型的实例，通过简单地改变参数值就能导致所有三种行为形式。此外，该模型具有解析易处理性这一巨大优势。我们的模型是非马尔可夫的，因为游走者的下一次跳跃（概率性地）由过去跳跃的历史决定。它还具有间歇性元素，因为在每一步有一种可能性是游走者根本不移动。由单个模型产生的这种丰富的综合情形为不同类型渐近行为的来源提供了有用的见解。
