Stationary measure induced by the eigenvalue problem of the one-dimensional Hadamard walk

2019/05/01 by Takashi Komatsu, Komatsu, Takashi, Norio Konno +1
Engineering · Mathematics · #FOS: Physical sciences #Quantum Physics (quant-ph) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1905.00330

openalex publication_date 2019/05/01 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

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.

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