论文标题
Riesz Walk的回报概率和自相似性
Return probability and self-similarity of the Riesz walk
论文作者
论文摘要
量子步行是随机步行的对应物。一个维度的2态量子步行可以通过复杂平面的单位圆上的度量来确定。至于单数连续测量，相应的量子步行的结果受到限制。在这种情况下，我们专注于Riesz Measure提供的量子步行，称为Riesz Walk，这是著名的连续措施之一。本文专门用于Riesz Walk的回报概率。此外，我们提出了一些关于步行的自相似性的猜想。
The quantum walk is a counterpart of the random walk. The 2-state quantum walk in one dimension can be determined by a measure on the unit circle in the complex plane. As for the singular continuous measure, results on the corresponding quantum walk are limited. In this situation, we focus on a quantum walk, called the Riesz walk, given by the Riesz measure which is one of the famous singular continuous measures. The present paper is devoted to the return probability of the Riesz walk. Furthermore, we present some conjectures on the self-similarity of the walk.
