论文标题
相关随机步行的过渡概率矩阵的特征多项式在图上
A Characteristic Polynomial for The Transition Probability Matrix of A Correlated Random Walk on A Graph
论文作者
论文摘要
我们定义了一个相关的随机步行（CRW），从Grover Walk的时间演化矩阵（Grover Matrix）上引起的相关随机步行（CRW），并通过使用确定的Zeta Zeta Zeta的Zeta Zeta函数的确定性表达来提供$ g $的特征性矩阵的特征多项式。作为应用，我们给出了从常规图和半毛线两部分图引起的CRW的过渡概率矩阵的光谱。此外，我们考虑了图上的另一种类型的CRW。
We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, 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 $G$. 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.
