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Volumn 9, Issue 1, 1999, Pages 1-13

Comparing eigenvalue bounds for Markov chains: When does Poincaré beat Cheeger?

Author keywords

Cheeger inequalitites; Eigenvalues; Groups; Markov chains; Poincar inequalities; Random walk; Trees

Indexed keywords


EID: 0033449690     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1029962594     Document Type: Article
Times cited : (14)

References (23)
  • 1
    • 0002103664 scopus 로고
    • On the Markov chain simulation method for uniform combinatorial distributions and simulated annealing
    • ALDOUS, D. (1987). On the Markov chain simulation method for uniform combinatorial distributions and simulated annealing. Probab. Engrg. Inform. Sci. 1 33-46.
    • (1987) Probab. Engrg. Inform. Sci. , vol.1 , pp. 33-46
    • Aldous, D.1
  • 2
    • 51249173340 scopus 로고
    • Eigenvalues and expanders
    • ALON, N. (1986). Eigenvalues and expanders. Combinatorica 6 83-96.
    • (1986) Combinatorica , vol.6 , pp. 83-96
    • Alon, N.1
  • 3
    • 33750994100 scopus 로고
    • 1, isoperimetric inequalities for graphs, and superconcentrators
    • 1, isoperimetric inequalities for graphs, and superconcentrators. J. Combin. Theory Ser. B 38 73-88.
    • (1985) J. Combin. Theory Ser. B , vol.38 , pp. 73-88
    • Alon, N.1    Millman, V.D.2
  • 5
    • 0003882879 scopus 로고    scopus 로고
    • Amer. Math. Soc., Providence, RI
    • CHUNG, F. (1997). Spectral Graph Theory. Amer. Math. Soc., Providence, RI.
    • (1997) Spectral Graph Theory
    • Chung, F.1
  • 7
    • 0001076208 scopus 로고
    • Comparison techniques for random walk on finite groups
    • DIACONIS, P. and SALOFF-COSTE, L. (1993a). Comparison techniques for random walk on finite groups. Ann. Probab. 21 2131-2156.
    • (1993) Ann. Probab. , vol.21 , pp. 2131-2156
    • Diaconis, P.1    Saloff-Coste, L.2
  • 8
    • 0000255332 scopus 로고
    • Comparison theorems for reversible Markov chains
    • DIACONIS, P. and SALOFF-COSTE, L. (1993b). Comparison theorems for reversible Markov chains. Ann. Appl. Probab. 3 696-730.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 696-730
    • Diaconis, P.1    Saloff-Coste, L.2
  • 9
    • 0002031070 scopus 로고
    • Moderate growth and random walk on finite groups
    • DIACONIS, P. and SALOFF-COSTE, L. (1994). Moderate growth and random walk on finite groups. Geom. Funct. Anal. 4 1-36.
    • (1994) Geom. Funct. Anal. , vol.4 , pp. 1-36
    • Diaconis, P.1    Saloff-Coste, L.2
  • 10
    • 0030487036 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for finite Markov chains
    • DIACONIS, P. and SALOFF-COSTE, L. (1996a). Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 695-750.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 695-750
    • Diaconis, P.1    Saloff-Coste, L.2
  • 11
    • 21344458979 scopus 로고    scopus 로고
    • Nash inequalities for finite Markov chains
    • DIACONIS, P. and SALOFF-COSTE, L. (1996b). Nash inequalities for finite Markov chains. J. Theoret. Probab. 9 459-510.
    • (1996) J. Theoret. Probab. , vol.9 , pp. 459-510
    • Diaconis, P.1    Saloff-Coste, L.2
  • 12
    • 0003373175 scopus 로고
    • Generating a random permutation with random transpositions
    • DIACONIS, P. and SHAHSHAHANI, M. (1981). Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Gebiete. 57 159-179.
    • (1981) Z. Wahrsch. Verw. Gebiete. , vol.57 , pp. 159-179
    • Diaconis, P.1    Shahshahani, M.2
  • 13
    • 0002740591 scopus 로고
    • Geometric bounds for eigenvalues of Markov chains
    • DIACONIS, P. and STROOCK, D. (1991). Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Probab. 1 36-61.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 36-61
    • Diaconis, P.1    Stroock, D.2
  • 15
    • 0024904712 scopus 로고
    • Approximating the permanent
    • JERRUM, M. and SINCLAIR, A. (1989). Approximating the permanent. SIAM J. Comput. 18 1149-1178.
    • (1989) SIAM J. Comput. , vol.18 , pp. 1149-1178
    • Jerrum, M.1    Sinclair, A.2
  • 16
    • 0031481570 scopus 로고    scopus 로고
    • A semidefinite bound for mixing rates of Markov chains
    • To appear
    • KAHALE, N. (1997). A semidefinite bound for mixing rates of Markov chains. Random Structures Algorithms. To appear. (Preliminary version appears in Lecture Notes in Comput. Sci. 1084 190-203. Springer, Berlin.)
    • (1997) Random Structures Algorithms
    • Kahale, N.1
  • 17
    • 84947909878 scopus 로고    scopus 로고
    • Preliminary version appears. Springer, Berlin
    • KAHALE, N. (1997). A semidefinite bound for mixing rates of Markov chains. Random Structures Algorithms. To appear. (Preliminary version appears in Lecture Notes in Comput. Sci. 1084 190-203. Springer, Berlin.)
    • Lecture Notes in Comput. Sci. , vol.1084 , pp. 190-203
  • 20
    • 0040264545 scopus 로고
    • On the maximum degree in a random tree
    • MOON, J. W. (1968). On the maximum degree in a random tree. Michigan Math. J. 15 429-432.
    • (1968) Michigan Math. J. , vol.15 , pp. 429-432
    • Moon, J.W.1
  • 22
    • 84971804758 scopus 로고
    • Improved bounds for mixing rates of Markov chains and multicommodity flow
    • SINCLAIR, A. (1992). Improved bounds for mixing rates of Markov chains and multicommodity flow. Combin. Probab. Comput. 1 351-370.
    • (1992) Combin. Probab. Comput. , vol.1 , pp. 351-370
    • Sinclair, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.