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

在这项研究中，我们集中在离散时间和连续时间的量子行走的各种图，包括随机图的转移概率的分析。对于离散时间情形，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。对于连续时间的情况下，我们显示局部图的结构和转移概率的拉普拉斯矩阵的特征空间的详细研究之间的关系。

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.