Spectral Analysis of Growing Graphs (eBook, PDF)
Nobuaki Obata
eBook, PDF

Spectral Analysis of Growing Graphs (eBook, PDF)

A Quantum Probability Point of View

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This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decompositi...

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