A study on relationships between stochastic and quantum models and random graph structures

在本研究中，我们集中分析了离散时间和连续时间量子行走在包括随机图在内的各种图上的跃迁概率。对于离散情况，通过对Jacobi矩阵特征空间的详细研究，得到了转移概率长时间平均的一些极限定理。对于连续时间情况，通过对拉普拉斯矩阵特征空间的详细研究，给出了局部图结构与转移概率之间的关系。

In this study, we concentrate on analysis of transition probabilities of discrete-time and continuous-time quantum walks on various graphs including random graphs. For the discrete-time case, we obtain some limit theorems for long-time average of the transition probabilities by detailed study of eigenspace of the Jacobi matrices. For the continuous-time case, we show relationships between local graph structures and the transition probabilities by detailed study of eigenspace of the Laplacian matrices.