A Characteristic Polynomial for The Transition Probability Matrix of A Correlated Random Walk on A Graph
Probability
2020-12-21 v2 Combinatorics
Abstract
We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph , and present a formula for the characteristic polynomial of the transition probability matrix of this CRW by using a determinant expression for the generalized weighted zeta function of . As applications, we give the spectrum of the transition probability matrices for the CRWs induced from the Grover matrices of regular graphs and semiregular bipartite graphs. Furthermore, we consider another type of the CRW on a graph.
Keywords
Cite
@article{arxiv.2012.09619,
title = {A Characteristic Polynomial for The Transition Probability Matrix of A Correlated Random Walk on A Graph},
author = {Takashi Komatsu and Norio Konno and Iwao Sato},
journal= {arXiv preprint arXiv:2012.09619},
year = {2020}
}
Comments
16 pages. arXiv admin note: text overlap with arXiv:2011.14162