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Volumn 360, Issue 2, 2008, Pages 899-923

Asymptotic spectral analysis of growing regular graphs

Author keywords

Adjacency matrix; Interacting fock space; Orthogonal polynomial; Quantum central limit theorem; Quantum decomposition; Spectral distribution

Indexed keywords


EID: 77950942369     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-07-04232-8     Document Type: Article
Times cited : (10)

References (38)
  • 1
    • 4944220790 scopus 로고    scopus 로고
    • Monotone independence, comb graphs and Bose-Einstein condensation
    • MR2085641 (2005f:81123)
    • L. Accardi, A. Ben Ghorbal and N. Obata, Monotone independence, comb graphs and Bose- Einstein condensation, Infin. Dimen. Anal. Quantum Probab. Relat. Top. 7 (2004), 419-435. MR2085641 (2005f:81123)
    • (2004) Infin. Dimen. Anal. Quantum Probab. Relat. Top. , vol.7 , pp. 419-435
    • Accardi, L.1    Ben Ghorbal, A.2    Obata, N.3
  • 2
    • 0000855365 scopus 로고    scopus 로고
    • Interacting Fock spaces and Gaussianization of probability measures
    • MR1665281 (2000d:60158)
    • L. Accardi and M. Bozejko, Interacting Fock spaces and Gaussianization of probability measures, Infin. Dimen. Anal. Quantum Probab. Relat. Top. 1 (1998), 663-670. MR1665281 (2000d:60158)
    • (1998) Infin. Dimen. Anal. Quantum Probab. Relat. Top. , vol.1 , pp. 663-670
    • Accardi, L.1    Bozejko, M.2
  • 5
    • 0013195416 scopus 로고    scopus 로고
    • Representations of symmetric groups and free probability
    • MR1644993 (2001b:05225)
    • P. Biane, Representations of symmetric groups and free probability, Adv. Math. 138 (1998), 126-181. MR1644993 (2001b:05225)
    • (1998) Adv. Math. , vol.138 , pp. 126-181
    • Biane, P.1
  • 6
    • 0004242420 scopus 로고
    • (2nd Ed.), Cambridge University Press. MR1271140 (95h:05105)
    • N. Biggs, Algebraic Graph Theory (2nd Ed.), Cambridge University Press, 1993. MR1271140 (95h:05105)
    • (1993) Algebraic Graph Theory
    • Biggs, N.1
  • 7
    • 0000259106 scopus 로고
    • Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
    • MR1038498 (91f:43011)
    • M. Bozejko, Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality, Studia Math. XCV (1989), 107-118. MR1038498 (91f:43011)
    • (1989) Studia Math. , vol.95 , pp. 107-118
    • Bozejko, M.1
  • 11
    • 0345741397 scopus 로고    scopus 로고
    • Central limit theorems for Coxeter systems and Artin systems of extra large type
    • MR2030209 (2004i:46096)
    • G. Fendler, Central limit theorems for Coxeter systems and Artin systems of extra large type, Infin. Dimen. Anal. Quantum Probab. Relat. Top. 6 (2003), 537-548. MR2030209 (2004i:46096)
    • (2003) Infin. Dimen. Anal. Quantum Probab. Relat. Top. , vol.6 , pp. 537-548
    • Fendler, G.1
  • 12
    • 0001610949 scopus 로고
    • z.ast;-algebra which has the metric approximation property
    • MR520930 (80j:46094)
    • z.ast;-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293. MR520930 (80j:46094)
    • (1979) Invent. Math. , vol.50 , pp. 279-293
    • Haagerup, U.1
  • 13
    • 0012803507 scopus 로고    scopus 로고
    • Deformations of the semicircle law derived from random walks on free groups
    • MR1671628 (2000f:60012)
    • Y. Hashimoto, Deformations of the semicircle law derived from random walks on free groups, Prob. Math. Stat. 18 (1998), 399-410. MR1671628 (2000f:60012)
    • (1998) Prob. Math. Stat. , vol.18 , pp. 399-410
    • Hashimoto, Y.1
  • 14
    • 0035618427 scopus 로고    scopus 로고
    • Quantum decomposition in discrete groups and interacting Fock spaces
    • MR1841622 (2003c:81102)
    • Y. Hashimoto, Quantum decomposition in discrete groups and interacting Fock spaces, Infin. Dimen. Anal. Quantum Probab. Relat. Top. 4 (2001), 277-287. MR1841622 (2003c:81102)
    • (2001) Infin. Dimen. Anal. Quantum Probab. Relat. Top. , vol.4 , pp. 277-287
    • Hashimoto, Y.1
  • 15
    • 0037250760 scopus 로고    scopus 로고
    • Central limit theorems for large graphs: Method of quantum decomposition
    • MR1946692 (2004f:81120)
    • Y. Hashimoto, A. Hora and N. Obata, Central limit theorems for large graphs: Method of quantum decomposition, J. Math. Phys. 44 (2003), 71-88. MR1946692 (2004f:81120)
    • (2003) J. Math. Phys. , vol.44 , pp. 71-88
    • Hashimoto, Y.1    Hora, A.2    Obata, N.3
  • 16
    • 0012889732 scopus 로고    scopus 로고
    • A quantum aspect of asymptotic spectral analysis of large Hamming graphs
    • Quantum Information III (T. Hida and K. Saitô, Eds.). MR1876329
    • Y. Hashimoto, N. Obata and N. Tabei, A quantum aspect of asymptotic spectral analysis of large Hamming graphs, Quantum Information III (T. Hida and K. Saitô, Eds.), World Scientific, 2001, pp. 45-57. MR1876329
    • (2001) World Scientific , pp. 45-57
    • Hashimoto, Y.1    Obata, N.2    Tabei, N.3
  • 17
    • 0005141929 scopus 로고    scopus 로고
    • The semicircle law, free random variables and entropy
    • MR1746976 (2001j:46099)
    • F. Hiai and D. Petz, The Semicircle Law, Free Random Variables and Entropy, Amer. Math. Soc., 2000. MR1746976 (2001j:46099)
    • (2000) Amer. Math. Soc.
    • Hiai, F.1    Petz, D.2
  • 18
    • 0012863563 scopus 로고    scopus 로고
    • Central limit theorems and asymptotic spectral analysis on large graphs
    • MR1628244 (99g:46089)
    • A. Hora, Central limit theorems and asymptotic spectral analysis on large graphs, Infin. Dimen. Anal. Quantum Probab. Relat. Top. 1 (1998), 221-246. MR1628244 (99g:46089)
    • (1998) Infin. Dimen. Anal. Quantum Probab. Relat. Top. , vol.1 , pp. 221-246
    • Hora, A.1
  • 19
    • 0032474669 scopus 로고    scopus 로고
    • Central limit theorem for the adjacency operators on the infinite symmetric group
    • MR1637801 (99i:46058)
    • A. Hora, Central limit theorem for the adjacency operators on the infinite symmetric group, Commun. Math. Phys. 195 (1998), 405-416. MR1637801 (99i:46058)
    • (1998) Commun. Math. Phys. , vol.195 , pp. 405-416
    • Hora, A.1
  • 20
    • 0034408313 scopus 로고    scopus 로고
    • Gibbs state on a distance-regular graph and its application to a scaling limit of the spectral distributions of discrete Laplacians
    • MR1785455 (2002c:05163)
    • A. Hora, Gibbs state on a distance-regular graph and its application to a scaling limit of the spectral distributions of discrete Laplacians, Probab. Theory Relat. Fields 118 (2000), 115-130. MR1785455 (2002c:05163)
    • (2000) Probab. Theory Relat. Fields , vol.118 , pp. 115-130
    • Hora, A.1
  • 21
    • 25144437579 scopus 로고    scopus 로고
    • A noncommutative version of Kerov's Gaussian limit for the Plancherel measure of the symmetric group
    • Asymptotic Combinatorics with Applications to Mathematical Physics (A. M. Vershik, Ed.), Springer, MR2009836 (2004k:60056)
    • A. Hora, A noncommutative version of Kerov's Gaussian limit for the Plancherel measure of the symmetric group, Asymptotic Combinatorics with Applications to Mathematical Physics (A. M. Vershik, Ed.), Lect. Notes in Math. Vol.1815, Springer, 2003, pp. 77-88. MR2009836 (2004k:60056)
    • (2003) Lect. Notes in Math. , vol.1815 , pp. 77-88
    • Hora, A.1
  • 22
    • 0037908736 scopus 로고    scopus 로고
    • Scaling limit for Gibbs states for Johnson graphs and resulting Meixner classes
    • MR1976874 (2004k:60057)
    • A. Hora, Scaling limit for Gibbs states for Johnson graphs and resulting Meixner classes, Infin. Dimen. Anal. Quantum Probab. Relat. Top. 6 (2003), 139-143. MR1976874 (2004k:60057)
    • (2003) Infin. Dimen. Anal. Quantum Probab. Relat. Top. , vol.6 , pp. 139-143
    • Hora, A.1
  • 23
    • 77950933501 scopus 로고    scopus 로고
    • Asymptotic spectral analysis on the Johnson graphs in infinite degree and zero temperature limit
    • MR2062187 (2005i:82032)
    • A. Hora, Asymptotic spectral analysis on the Johnson graphs in infinite degree and zero temperature limit, Interdiscip. Inform. Sci. 10 (2004), 1-10. MR2062187 (2005i:82032)
    • (2004) Interdiscip. Inform. Sci. , vol.10 , pp. 1-10
    • Hora, A.1
  • 24
    • 4944241451 scopus 로고    scopus 로고
    • Quantum decomposition and quantum central limit theorem
    • Fundamental Problems in Quantum Physics (L. Accardi and S. Tasaki, Eds.). MR2003920 (2004i:81131)
    • A. Hora and N. Obata, Quantum decomposition and quantum central limit theorem, Fundamental Problems in Quantum Physics (L. Accardi and S. Tasaki, Eds.), World Scientific, 2003, pp. 284-305. MR2003920 (2004i:81131)
    • (2003) World Scientific , pp. 284-305
    • Hora, A.1    Obata, N.2
  • 25
    • 77950950476 scopus 로고    scopus 로고
    • An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit
    • Quantum Information V (T. Hida and K. Saitô, Eds.), to appear. MR2210974
    • A. Hora and N. Obata, An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit, Quantum Information V (T. Hida and K. Saitô, Eds.), World Scientific, 2005, to appear. MR2210974
    • (2005) World Scientific
    • Hora, A.1    Obata, N.2
  • 28
    • 0040817484 scopus 로고
    • Gaussian limit for the Plancherel measure of the symmetric group
    • Série I, MR1204294 (93k:20106)
    • S. Kerov, Gaussian limit for the Plancherel measure of the symmetric group, C. R. Acad. Sci. Paris 316 Série I (1993), 303-308. MR1204294 (93k:20106)
    • (1993) C. R. Acad. Sci. Paris , Issue.316 , pp. 303-308
    • Kerov, S.1
  • 29
    • 33847574798 scopus 로고
    • Symmetric random walks on groups
    • MR0109367 (22:253)
    • H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354. MR0109367 (22:253)
    • (1959) Trans. Amer. Math. Soc. , vol.92 , pp. 336-354
    • Kesten, H.1
  • 30
    • 33748881482 scopus 로고    scopus 로고
    • Probability on discrete structures
    • H. Kesten (Ed.), Springer, MR2023649 (2004g:60003)
    • H. Kesten (Ed.), Probability on Discrete Structures, Encyclopaedia of Mathematical Sciences, Vol.110, Springer, 2004. MR2023649 (2004g:60003)
    • (2004) Encyclopaedia of Mathematical Sciences , vol.110
  • 31
    • 0000294458 scopus 로고
    • The expected eigenvalue distribution of a large regular graph
    • MR629617 (84h:05089)
    • B. D. McKay, The expected eigenvalue distribution of a large regular graph, Linear Alg. Appl. 40 (1981), 203-216. MR629617 (84h:05089)
    • (1981) Linear Alg. Appl. , vol.40 , pp. 203-216
    • McKay, B.D.1
  • 32
    • 33644982935 scopus 로고    scopus 로고
    • Quantum probabilistic approach to spectral analysis of star graphs
    • MR2062191 (2005a:05140)
    • N. Obata, Quantum probabilistic approach to spectral analysis of star graphs, Interdiscip. Inform. Sci. 10 (2004), 41-52. MR2062191 (2005a:05140)
    • (2004) Interdiscip. Inform. Sci. , vol.10 , pp. 41-52
    • Obata, N.1
  • 33
    • 65049090912 scopus 로고    scopus 로고
    • Notions of independence in quantum probability theory and spectral analysis of graphs
    • MR2125194 (2006f:46059)
    • N. Obata, Notions of independence in quantum probability theory and spectral analysis of graphs, Sugaku Expositions 57 (2005), 1-20. MR2125194 (2006f:46059)
    • (2005) Sugaku Expositions , vol.57 , pp. 1-20
    • Obata, N.1
  • 34
    • 0034711906 scopus 로고    scopus 로고
    • A q-deformed Poisson distribution based on orthogonal polynomials
    • MR1746884 (2001c:33034)
    • N. Saitoh and H. Yoshida, A q-deformed Poisson distribution based on orthogonal polynomials, J. Phys. A: Math. Gen. 33 (2000), 1435-1444. MR1746884 (2001c:33034)
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 1435-1444
    • Saitoh, N.1    Yoshida, H.2
  • 37
    • 0009137614 scopus 로고
    • Asymptotic combinatorics and algebraic analysis
    • (Zürich, 1994), Birkhäuser, Basel, MR1404040 (98e:60018)
    • A. M. Vershik, Asymptotic combinatorics and algebraic analysis, Proc. International Congress of Mathematicians, Vol.2 (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 1384-1394. MR1404040 (98e:60018)
    • (1995) Proc. International Congress of Mathematicians , vol.2 , pp. 1384-1394
    • Vershik, A.M.1
  • 38
    • 0003341427 scopus 로고
    • Free random variables
    • CRM Monograph Series. MR1217253 (94c:46133)
    • D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, Amer. Math. Soc., 1992. MR1217253 (94c:46133)
    • (1992) Amer. Math. Soc.
    • Voiculescu, D.1    Dykema, K.2    Nica, A.3


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