TY - JOUR
T1 - Asymptotic spectral analysis of growing regular graphs
AU - Hora, Akihito
AU - Obata, Nobuaki
PY - 2008/2
Y1 - 2008/2
N2 - We propose the quantum probabilistic techniques to ob tain the asymptotic spectral distribution of the adjacency matrix of a growing regular graph. We prove the quantum central limit theorem for the adjacency matrix of a growing regular graph in the vacuum and deformed vacuum states. The condition for the growth is described in terms of simple statistics arising from the stratification of the graph. The asymptotic spectral distribution of the adjacency matrix is obtained from the classical reduction.
AB - We propose the quantum probabilistic techniques to ob tain the asymptotic spectral distribution of the adjacency matrix of a growing regular graph. We prove the quantum central limit theorem for the adjacency matrix of a growing regular graph in the vacuum and deformed vacuum states. The condition for the growth is described in terms of simple statistics arising from the stratification of the graph. The asymptotic spectral distribution of the adjacency matrix is obtained from the classical reduction.
KW - Adjacency matrix
KW - Interacting fock space
KW - Orthogonal polynomial
KW - Quantum central limit theorem
KW - Quantum decomposition
KW - Spectral distribution
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U2 - 10.1090/S0002-9947-07-04232-8
DO - 10.1090/S0002-9947-07-04232-8
M3 - Article
AN - SCOPUS:77950942369
SN - 0002-9947
VL - 360
SP - 899
EP - 923
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -