LEADER 03598nam  22005775  450 
001 9910165139203321
005 20220421171820.0
010   $a981-10-3506-7
024 7 $a10.1007/978-981-10-3506-7
035   $a(CKB)3710000001065142
035   $a(DE-He213)978-981-10-3506-7
035   $a(MiAaPQ)EBC4810073
035   $a(PPN)19886678X
035   $a(EXLCZ)993710000001065142
100   $a20170217d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aSpectral analysis of growing graphs $ea quantum probability point of view /$fby Nobuaki Obata
205   $a1st ed. 2017.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2017.
215   $a1 online resource (VIII, 138 p. 22 illus., 9 illus. in color.)
225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v20
311   $a981-10-3505-9 
320   $aIncludes bibliographical references and index.
327   $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.
330   $aThis book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.
410  0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v20
606   $aMathematical physics
606   $aProbabilities
606   $aGraph theory
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020
615  0$aMathematical physics.
615  0$aProbabilities.
615  0$aGraph theory.
615 14$aMathematical Physics.
615 24$aProbability Theory and Stochastic Processes.
615 24$aGraph Theory.
676   $a515.7222
700   $aObata$b Nobuaki$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441106
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910165139203321
996   $aSpectral Analysis of Growing Graphs$91562287
997   $aUNINA