Stationary Measure Induced by the Eigenvalue Problem of the One-Dimensional Hadamard Walk
Stationary Measure Induced by the Eigenvalue Problem of the One-Dimensional Hadamard Walk
复制标题
一维Hadamard行走特征值问题引起的平稳测度
DOI：
10.1007/s10955-022-02901-x
复制
发表时间：
2022
影响因子：
1.6
通讯作者：
Konno Norio
中科院分区：
文献类型：
--
作者：
Komatsu Takashi;Konno Norio
本文考虑了一维整数格上Hadamard游动的平稳测度。在这里，通过求解特征值问题所给出的所有定常度量都是通过传递矩阵方法完全确定的。然后将这些平稳度量分为三类，即二次多项式、有界和指数型。特别地，我们给出了有界型平稳测度是周期的一个明确的充要条件。
In this paper, we consider the stationary measure of the Hadamard walk on the one-dimensional integer lattice. Here all the stationary measures given by solving the eigenvalue problem are completely determined via the transfer matrix method. Then these stationary measures can be divided into three classes, i.e., quadratic polynomial, bounded, and exponential types. In particular, we present an explicit necessary and sufficient condition for the bounded-type stationary measure to be periodic.