메뉴 건너뛰기




Volumn 41, Issue 43, 2008, Pages

Eigenvectors of the discrete Laplacian on regular graphs - A statistical approach

Author keywords

[No Author keywords available]

Indexed keywords


EID: 56549098621     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/43/435203     Document Type: Article
Times cited : (24)

References (30)
  • 2
    • 0242337473 scopus 로고    scopus 로고
    • Mixing times
    • Lovsz L and Winkler P 1998 Mixing times Microsurveys in Discrete Probability (Princeton, NJ, 1997) (DIMACS Ser. Discrete Math. Theoret. Comput. Sci. vol 41) (Providence, RI: American Mathematical Society) pp 85-133
    • (1998) Microsurveys in Discrete Probability , pp. 85-133
    • Lovsz, L.1    Winkler, P.2
  • 3
    • 0344077919 scopus 로고    scopus 로고
    • Finite metric spaces-combinatorics, geometry and algorithms
    • Linial N 2002 Finite metric spaces-combinatorics, geometry and algorithms Proc. Int. Congress of Mathematicians, vol III (Beijing, 2002) (Beijing: Higher Education Press) pp 573-86
    • (2002) Proc. Int. Congress of Mathematicians, Vol III , pp. 573-586
    • Linial, N.1
  • 4
    • 0030283874 scopus 로고    scopus 로고
    • Linear-time encodable and decodable error-correcting codes
    • Spielman D A 1996 Linear-time encodable and decodable error-correcting codes IEEE Trans. Inf. Theory 42 1723-31 (codes and complexity)
    • (1996) IEEE Trans. Inf. Theory , vol.42 , Issue.6 , pp. 1723-1731
    • Spielman, D.A.1
  • 6
    • 56549124593 scopus 로고    scopus 로고
    • Perspectives and challenges to harmonic analysis and geometry in high dimensions: Geometric diffusions as a tool for harmonic analysis and structure definition of data
    • Coifman R R 2005 Perspectives and challenges to harmonic analysis and geometry in high dimensions: geometric diffusions as a tool for harmonic analysis and structure definition of data Perspectives in Analysis (Math. Phys. Stud. vol 27) (Berlin: Springer) pp 27-35
    • (2005) Perspectives in Analysis , vol.27 , pp. 27-35
    • Coifman, R.R.1
  • 7
    • 0000812783 scopus 로고
    • Partitioning sparse matrices with eigenvectors of graphs
    • Pothen A, Simon H D and Liou K P 1990 Partitioning sparse matrices with eigenvectors of graphs SIAM J. Matrix Anal. Appl. 11 430-52
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , Issue.3 , pp. 430-452
    • Pothen, A.1    Simon, H.D.2    Liou, K.P.3
  • 10
    • 34250768646 scopus 로고    scopus 로고
    • Quantum chaos on discrete graphs
    • Smilansky U 2007 Quantum chaos on discrete graphs J. Phys. A: Math. Theor. 40 F621-30
    • (2007) J. Phys. A: Math. Theor. , vol.40 , Issue.27
    • Smilansky, U.1
  • 11
    • 0000450808 scopus 로고
    • Regular and irregular semiclassical wavefunctions
    • Berry M V 1977 Regular and irregular semiclassical wavefunctions J. Phys. A: Math. Gen. 10 2083-91
    • (1977) J. Phys. A: Math. Gen. , vol.10 , Issue.12 , pp. 2083-2091
    • Berry, M.V.1
  • 12
    • 42749104942 scopus 로고    scopus 로고
    • Semiclassical construction of random wave functions for confined systems
    • Urbina J D and Richter K 2004 Semiclassical construction of random wave functions for confined systems Phys. Rev. E 70 015201
    • (2004) Phys. Rev. , vol.70 , Issue.1 , pp. 015201
    • Urbina, J.D.1    Richter, K.2
  • 13
    • 0037128791 scopus 로고    scopus 로고
    • Nodal domains statistics: A criterion for quantum chaos
    • Blum G, Gnutzmann S and Smilansky U 2002 Nodal domains statistics: a criterion for quantum chaos Phys. Rev. Lett. 88 114101
    • (2002) Phys. Rev. Lett. , vol.88 , Issue.11 , pp. 114101
    • Blum, G.1    Gnutzmann, S.2    Smilansky, U.3
  • 14
    • 50249159793 scopus 로고    scopus 로고
    • Geometric characterization of nodal domains: The area-to-perimeter ratio
    • Elon Y, Gnutzmann S, Joas C and Smilansky U 2007 Geometric characterization of nodal domains: the area-to-perimeter ratio J. Phys. A: Math. Theor. 40 2689-707
    • (2007) J. Phys. A: Math. Theor. , vol.40 , Issue.11 , pp. 2689-2707
    • Elon, Y.1    Gnutzmann, S.2    Joas, C.3    Smilansky, U.4
  • 15
    • 85012603843 scopus 로고
    • A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
    • Bollobs B 1980 A probabilistic proof of an asymptotic formula for the number of labelled regular graphs Eur. J. Comb. 1 311-6
    • (1980) Eur. J. Comb. , vol.1 , pp. 311-316
    • Bollobs, B.1
  • 16
    • 51249183803 scopus 로고
    • The diameter of random regular graphs
    • Bollobs B and De la Vega W F 1982 The diameter of random regular graphs Combinatorica 2 125-34
    • (1982) Combinatorica , vol.2 , Issue.2 , pp. 125-134
    • Bollobs, B.1    De La Vega, W.F.2
  • 17
    • 0000294458 scopus 로고
    • The expected eigenvalue distribution of a large regular graph
    • McKay B D 1981 The expected eigenvalue distribution of a large regular graph Linear Algebr. Appl. 40 203-16
    • (1981) Linear Algebr. Appl. , vol.40 , Issue.1 , pp. 203-216
    • McKay, B.D.1
  • 19
    • 79959409062 scopus 로고    scopus 로고
    • Nodal domains on graphs-how to count them and why?
    • Band R, Oren I and Smilansky U 2008 Nodal domains on graphs-how to count them and why? Analysis on Graphs and its Applications (Proc. Symp. Pure Math.) (Providence, RI: American Mathematical Society) pp 5-28
    • (2008) Analysis on Graphs and Its Applications , pp. 5-28
    • Band, R.1    Oren, I.2    Smilansky, U.3
  • 20
    • 33846137645 scopus 로고    scopus 로고
    • Faber-{K}rahn type inequalities for trees
    • Biyikolu T and Leydold J 2007 Faber-{K}rahn type inequalities for trees J. Comb. Theory Ser. B 97 159-74
    • (2007) J. Comb. Theory Ser. , vol.97 , Issue.2 , pp. 159-174
    • Biyikolu, T.1    Leydold, J.2
  • 24
    • 0033444831 scopus 로고    scopus 로고
    • Generating random regular graphs quickly
    • Steger A and Wormald N C 1999 Generating random regular graphs quickly Comb. Probab. Comput. 8 377-96 (Random Graphs and Combinatorial Structures (Oberwolfach, 1997))
    • (1999) Comb. Probab. Comput. , vol.8 , Issue.4 , pp. 377-396
    • Steger, A.1    Wormald, N.C.2
  • 26
    • 0039318563 scopus 로고
    • Sur les écarts de la courbe de distribution empirique
    • Smirnov N 1939 Sur les écarts de la courbe de distribution empirique Recueil Mathématique 6 3-26
    • (1939) Recueil Mathématique , vol.6 , pp. 3-26
    • Smirnov, N.1
  • 27
    • 0001341675 scopus 로고
    • Numerical computation of multivariate normal probabilities
    • Genz A 1992 Numerical computation of multivariate normal probabilities J. Comput. Graph Stat. 1 141-50
    • (1992) J. Comput. Graph Stat. , vol.1 , Issue.2 , pp. 141-150
    • Genz, A.1
  • 28
    • 56549126598 scopus 로고    scopus 로고
    • Genz A http://www.math.wsu.edu/faculty/genz/homepage
    • Genz, A.1
  • 29
    • 38049037486 scopus 로고    scopus 로고
    • Eigenvectors of random graphs: Nodal domains
    • Dekel Y, Lee J and Linial N 2007 Eigenvectors of random graphs: nodal domains APPROX-RANDOM pp 436-48
    • (2007) APPROX-RANDOM , pp. 436-448
    • Dekel, Y.1    Lee, J.2    Linial, N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.