메뉴 건너뛰기




Volumn 6, Issue 3, 1996, Pages 695-750

Logarithmic Sobolev inequalities for finite Markov chains

Author keywords

Logarithmic Sobolev inequalities; Markov chains

Indexed keywords


EID: 0030487036     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968224     Document Type: Article
Times cited : (446)

References (51)
  • 1
    • 38249036545 scopus 로고
    • Strong uniform times and finite random walks
    • ALDOUS, D. and DIACONIS, P. (1987). Strong uniform times and finite random walks. Adv. in Appl. Math. 8 69-97.
    • (1987) Adv. in Appl. Math. , vol.8 , pp. 69-97
    • Aldous, D.1    Diaconis, P.2
  • 2
    • 51249173340 scopus 로고
    • Eigenvalues and expanders
    • ALON, N. (1987). Eigenvalues and expanders. Combinatorica 5 83-96.
    • (1987) Combinatorica , vol.5 , 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 78-88.
    • (1985) J. Combin. Theory Ser. B , vol.38 , pp. 78-88
    • Alon, N.1    Milman, V.2
  • 5
    • 0002925263 scopus 로고
    • L'hypercontractivité et son utilisation en théorie des semigroups
    • Springer, Berlin
    • BAKRY, D. (1994). L'hypercontractivité et son utilisation en théorie des semigroups. Ecole d'Été de Saint Flour 1992. Lecture Notes in Math. 1581. Springer, Berlin.
    • (1994) Ecole D'été de Saint Flour 1992. Lecture Notes in Math. , vol.1581
    • Bakry, D.1
  • 6
    • 85012603843 scopus 로고
    • A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
    • BOLLOBAS, B. (1980). A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. European J. Combin. 1 311-316.
    • (1980) European J. Combin. , vol.1 , pp. 311-316
    • Bollobas, B.1
  • 11
    • 0001076208 scopus 로고
    • Comparison techniques for random walk on finite groups
    • DIACONIS, P. and SALOFF-COSTE, L. (1993). 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
  • 12
    • 0000255332 scopus 로고
    • Comparison theorems for reversible Markov chains
    • DIACONIS, P. and SALOFF-COSTE, L. (1993). 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
  • 15
    • 21344457258 scopus 로고
    • An application of Harnack inequalities to random walk on nilpotent quotients
    • DIACONIS, P. and SALOFF-COSTE, L. (1995). An application of Harnack inequalities to random walk on nilpotent quotients. Journal of Fourier Analysis and Its Applications (Kahane special issue) 189-207.
    • (1995) Journal of Fourier Analysis and Its Applications , Issue.KAHANE SPEC. ISSUE , pp. 189-207
    • Diaconis, P.1    Saloff-Coste, L.2
  • 16
    • 0001892785 scopus 로고
    • Random walks on finite groups: A survey of analytic techniques
    • (H. Heyer, ed.) World Scientific, Singapore
    • DIACONIS, P. and SALOFF-COSTE, L. (1995). Random walks on finite groups: a survey of analytic techniques. In Probability Measures on Groups and Related Structures 11 (H. Heyer, ed.) 46-75. World Scientific, Singapore.
    • (1995) Probability Measures on Groups and Related Structures , vol.11 , pp. 46-75
    • Diaconis, P.1    Saloff-Coste, L.2
  • 19
    • 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
  • 20
    • 0003119203 scopus 로고
    • Time to reach stationarity in the Bernoulli-Laplace diffusion model
    • DIACONIS, P. and SHAHSHAHANI, M. (1987). Time to reach stationarity in the Bernoulli-Laplace diffusion model. SIAM J. Math. Anal. 18 208-218.
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 208-218
    • Diaconis, P.1    Shahshahani, M.2
  • 21
    • 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
  • 23
    • 0002590276 scopus 로고
    • Eigenvalue bounds on convergence to stationarity for nonversible Markov chains, with application to the exclusion process
    • FILL, J. (1991). Eigenvalue bounds on convergence to stationarity for nonversible Markov chains, with application to the exclusion process. Ann. Appl. Probab. 1 62-87.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 62-87
    • Fill, J.1
  • 24
    • 0001429116 scopus 로고
    • Logarithmic Sobolev inequalities
    • GROSS, L. (1976). Logarithmic Sobolev inequalities. Amer. J. Math. 97 1061-1083.
    • (1976) Amer. J. Math. , vol.97 , pp. 1061-1083
    • Gross, L.1
  • 25
    • 0002236459 scopus 로고
    • Logarithmic Sobolev inequalities and contractivity properties of semigroups
    • Springer, Berlin
    • GROSS, L. (1993). Logarithmic Sobolev inequalities and contractivity properties of semigroups. Lecture Notes in Math. 1563. Springer, Berlin.
    • (1993) Lecture Notes in Math. , vol.1563
    • Gross, L.1
  • 27
    • 0001359676 scopus 로고
    • Logarithmic Sobolev inequalities and stochastic ising models
    • HOLLEY, R. and STROOCK, D. (1987). Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46 1159-1194.
    • (1987) J. Statist. Phys. , vol.46 , pp. 1159-1194
    • Holley, R.1    Stroock, D.2
  • 30
    • 84968494166 scopus 로고
    • An example in the theory of hypercontractive semigroups
    • KORZENIOWSKI, A. and STROOCK, D. (1985). An example in the theory of hypercontractive semigroups. Proc. Amer. Math. Soc. 94 87-90.
    • (1985) Proc. Amer. Math. Soc. , vol.94 , pp. 87-90
    • Korzeniowski, A.1    Stroock, D.2
  • 32
    • 21144481999 scopus 로고
    • Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics
    • LU, S. L. and YAU, H. T. (1993). Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Comm. Math. Phys. 161 399-433.
    • (1993) Comm. Math. Phys. , vol.161 , pp. 399-433
    • Lu, S.L.1    Yau, H.T.2
  • 34
    • 0000789645 scopus 로고
    • Explicit construction of concentrators
    • MARGULIS, G. (1973). Explicit construction of concentrators. Problemy Peredachi Informatsii 9 71-80. [English transl. Problems of Information Transmission (1975), 325-332.]
    • (1973) Problemy Peredachi Informatsii , vol.9 , pp. 71-80
    • Margulis, G.1
  • 35
    • 0040367266 scopus 로고
    • English transl.
    • MARGULIS, G. (1973). Explicit construction of concentrators. Problemy Peredachi Informatsii 9 71-80. [English transl. Problems of Information Transmission (1975), 325-332.]
    • (1975) Problems of Information Transmission , pp. 325-332
  • 38
    • 84990628122 scopus 로고
    • Diffusion of colour in the simple exclusion process
    • QUASTEL, J. (1992). Diffusion of colour in the simple exclusion process. Comm. Pure Appl. Math. 45 623-679.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 623-679
    • Quastel, J.1
  • 39
    • 84968517521 scopus 로고
    • Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators
    • ROTHAUS, O. (1980). Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators. J. Funct. Anal. 39 42-56.
    • (1980) J. Funct. Anal. , vol.39 , pp. 42-56
    • Rothaus, O.1
  • 40
    • 0000247778 scopus 로고
    • Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities
    • ROTHAUS, O. (1981). Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities. J. Funct. Anal. 42 102-109.
    • (1981) J. Funct. Anal. , vol.42 , pp. 102-109
    • Rothaus, O.1
  • 41
    • 0000247777 scopus 로고
    • Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators
    • ROTHAUS, O. (1981). Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators. J. Funct. Anal. 42 110-120.
    • (1981) J. Funct. Anal. , vol.42 , pp. 110-120
    • Rothaus, O.1
  • 42
    • 51249168651 scopus 로고
    • Precise estimates on the rate at which certain diffusions tend to equilibrium
    • SALOFF-COSTE, L. (1994). Precise estimates on the rate at which certain diffusions tend to equilibrium. Math. Z. 217 641-677.
    • (1994) Math. Z. , vol.217 , pp. 641-677
    • Saloff-Coste, L.1
  • 44
    • 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. Combinatorics, Probability and Computing 1 351-370.
    • (1992) Combinatorics, Probability and Computing , vol.1 , pp. 351-370
    • Sinclair, A.1
  • 48
    • 0002236462 scopus 로고
    • Logarithmic Sobolev inequalities for Gibbs states
    • Springer, Berlin
    • STROOCK, D. (1993). Logarithmic Sobolev inequalities for Gibbs states. Lecture Notes in Math. 1563. Springer, Berlin.
    • (1993) Lecture Notes in Math. , vol.1563
    • Stroock, D.1
  • 49
    • 0000284028 scopus 로고
    • The logarithmic Sobolev inequality for discrete spin systems on a lattice
    • STROOCK, D. and ZEGARLINSKI, B. (1992). The logarithmic Sobolev inequality for discrete spin systems on a lattice. Comm. Math. Phys. 149 175-193.
    • (1992) Comm. Math. Phys. , vol.149 , pp. 175-193
    • Stroock, D.1    Zegarlinski, B.2
  • 50
    • 0039182748 scopus 로고
    • Ph.D. dissertation, Harvard Univ
    • SU, F. (1995). Ph.D. dissertation, Harvard Univ.
    • (1995)
    • Su, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.