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020 _a9789811035067
_9978-981-10-3506-7
024 7 _a10.1007/978-981-10-3506-7
_2doi
040 _cCUS
050 4 _aQA401-425
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.15
_223
100 1 _aObata, Nobuaki.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSpectral Analysis of Growing Graphs
_h[electronic resource] :
_bA Quantum Probability Point of View /
_cby Nobuaki Obata.
250 _a1st ed. 2017.
264 1 _aSingapore :
_bSpringer Singapore :
_bImprint: Springer,
_c2017.
300 _aVIII, 138 p. 22 illus., 9 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Mathematical Physics,
_x2197-1757 ;
_v20
505 0 _a1. Graphs and Matrices -- 2. Spectra of Finite Graphs -- 3. Spectral Distributions of Graphs -- 4. Orthogonal Polynomials and Fock Spaces -- 5. Analytic Theory of Moments -- 6. Method of Quantum Decomposition -- 7. Graph Products and Asymptotics -- References -- Index.
520 _aThis 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 decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.
650 0 _aMathematical physics.
650 0 _aProbabilities.
650 0 _aGraph theory.
650 1 4 _aMathematical Physics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M35000
650 2 4 _aProbability Theory and Stochastic Processes.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M27004
650 2 4 _aGraph Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M29020
830 0 _aSpringerBriefs in Mathematical Physics,
_x2197-1757 ;
_v20
856 4 0 _uhttps://doi.org/10.1007/978-981-10-3506-7
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
942 _cEBK
999 _c205879
_d205879