A Quantum Probability Approach To Asymptotic Spectral Analysis Of Growing Regular Graphs

Quantum probability theory is a crystallization of classical probability theory and quantum mechanics which are mutual cross, mutual penetration, and it is also a kind of non commutative probability theory on the level of operator. This paper discusses asymptotic spectral distribution of graphs by using approach of quantum probability theory, the main work include applying quantum probability approach to give a quan-tum decomposition of adjacency matrix(operator) of growing regular graphs; and for growing regular graphs, we prove quantum center limit theorems in the vacuum state for the corresponding.The content of this paper includes the following three chapters:Chapter 1 introduction,we shortly introduce the research history and development status of quantum probability,and quote about the basic knowledge of quantum prob-ability.Chapter 2 We discuss the independence in the quantum probability space and we also prove the quantum central limit theorems with respect to it.Chapter 3 We discuss the concrete applications of quantum probability approach for asymptotic spectral analysis of graphs.