Titlebook: Quantum Probability and Spectral Analysis of Graphs; Akihito Hora,Nobuaki Obata Book 2007 Springer-Verlag Berlin Heidelberg 2007 Graph The

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Akihito Hora Dr.,Nobuaki Obata Dr. these changes is economic growth, which is a consequence of external (globalisation) and internal factors (liberalisation and economic reform since the early 1990s) – both interrelated. Along with economic development, there are other dimensions of social and environmental change, such as rapid urb

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978-3-642-08026-5Springer-Verlag Berlin Heidelberg 2007

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Quantum Probability and Orthogonal Polynomials,This chapter is devoted to most basic notions and results in quantum probability theory, especially concerning the interplay of (one-mode) interacting Fock spaces and orthogonal polynomials.

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Adjacency Matrices,In this chapter we study the adjacency matrix of a graph and an appropriate algebraic probability space in which it lives. Especially the vacuum state and their deformation on the adjacency algebra are treated. In Sect. 2.4 we introduce the . of the adjacency matrix, which will play a key role throughout this book.

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Homogeneous Trees,We shall go further through the general results developed in the preceding chapter to investigate spectral properties of a homogeneous tree and its variant in a quite explicit manner. The central limit distributions obtained from such growing graphs include the Wigner semicircle law, free Poisson distributions and free Meixner laws.