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Volumn 32, Issue 3 B, 2004, Pages 2526-2544

Measure concentration for Euclidean distance in the case of dependent random variables

Author keywords

Dobrushin Shlosman mixing condition; Gibbs sampler; Measure concentration; Relative entropy; Wasserstein distance

Indexed keywords


EID: 4544232692     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117904000000702     Document Type: Article
Times cited : (29)

References (21)
  • 2
    • 0035638785 scopus 로고    scopus 로고
    • Hypercontractivity of Hamilton-Jacobi equations
    • BOBKOV, S., GENTIL, I. and LEDOUX, M. (2001). Hypercontractivity of Hamilton-Jacobi equations. J. Math. Pures Appl. (9) 80 669-696.
    • (2001) J. Math. Pures Appl. (9) , vol.80 , pp. 669-696
    • Bobkov, S.1    Gentil, I.2    Ledoux, M.3
  • 3
    • 0002829137 scopus 로고    scopus 로고
    • Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
    • BOBKOV, S. and GÖTZE, F. (1999). Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal. 163 1-28.
    • (1999) J. Funct. Anal. , vol.163 , pp. 1-28
    • Bobkov, S.1    Götze, F.2
  • 4
    • 0000627593 scopus 로고    scopus 로고
    • On log-Sobolev inequalities for unbounded spin systems
    • BODINEAU, TH. and HELFFER, B. (1999). On log-Sobolev inequalities for unbounded spin systems. J. Funct. Anal. 166 168-178.
    • (1999) J. Funct. Anal. , vol.166 , pp. 168-178
    • Bodineau, T.H.1    Helffer, B.2
  • 5
    • 0000080779 scopus 로고
    • Prescribing a system of random variables by conditional distributions
    • DOBRUSHIN, R. L. (1970). Prescribing a system of random variables by conditional distributions. Theory Probab. Appl. 15 453-486.
    • (1970) Theory Probab. Appl. , vol.15 , pp. 453-486
    • Dobrushin, R.L.1
  • 6
    • 0002498186 scopus 로고
    • Constructive criterion for the uniqueness of Gibbs field
    • (J. Fritz, A. Jaffe and D. Szász, eds.). Birkhäuser, Basel
    • DOBRUSHIN, R. L. and SHLOSMAN, S. (1985a). Constructive criterion for the uniqueness of Gibbs field. In Statistical Physics and Dynamical Systems (J. Fritz, A. Jaffe and D. Szász, eds.) 347-369. Birkhäuser, Basel.
    • (1985) Statistical Physics and Dynamical Systems , pp. 347-369
    • Dobrushin, R.L.1    Shlosman, S.2
  • 7
    • 0002498186 scopus 로고
    • Completely analytical Gibbs fields
    • (J. Fritz, A. Jaffe and D. Szász, eds.). Birkhäuser, Basel
    • DOBRUSHIN, R. L. and SHLOSMAN, S. (1985b). Completely analytical Gibbs fields. In Statistical Physics and Dynamical Systems (J. Fritz, A. Jaffe and D. Szász, eds.) 347-369. Birkhäuser, Basel.
    • (1985) Statistical Physics and Dynamical Systems , pp. 347-369
    • Dobrushin, R.L.1    Shlosman, S.2
  • 8
    • 0001217140 scopus 로고
    • Completely analytical interactions: Constructive description
    • DOBRUSHIN, R. L. and SHLOSMAN, S. (1987). Completely analytical interactions: Constructive description. J. Statist. Phys. 46 983-1014.
    • (1987) J. Statist. Phys. , vol.46 , pp. 983-1014
    • Dobrushin, R.L.1    Shlosman, S.2
  • 10
    • 0033161965 scopus 로고    scopus 로고
    • Remarks on decay of correlation and Witten-Laplacians III. Application to logarithmic Sobolev inequalities
    • HELFFER, B. (1999). Remarks on decay of correlation and Witten-Laplacians III. Application to logarithmic Sobolev inequalities. Ann. Inst. H. Poincaré Probab. Statist. 35 483-508.
    • (1999) Ann. Inst. H. Poincaré Probab. Statist. , vol.35 , pp. 483-508
    • Helffer, B.1
  • 11
    • 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. 16 1159-1191.
    • (1987) J. Statist. Phys. , vol.16 , pp. 1159-1191
    • Holley, R.1    Stroock, D.2
  • 13
    • 0022720166 scopus 로고
    • A simple proof of the blowing-up lemma
    • MARTON, K. (1986). A simple proof of the blowing-up lemma. IEEE Trans. Inform. Theory 32 445-446.
    • (1986) IEEE Trans. Inform. Theory. , vol.32 , pp. 445-446
    • Marton, K.1
  • 14
    • 0030514042 scopus 로고    scopus 로고
    • Bounding d̄-distance by informational divergence: A method to prove measure concentration
    • MARTON, K. (1996). Bounding d̄-distance by informational divergence: A method to prove measure concentration. Ann. Probab. 24 857-866.
    • (1996) Ann. Probab. , vol.24 , pp. 857-866
    • Marton, K.1
  • 15
    • 0032021367 scopus 로고    scopus 로고
    • Measure concentration for a class of random processes
    • MARTON, K. (1998). Measure concentration for a class of random processes. Probab. Theory Related Fields 110 427-439.
    • (1998) Probab. Theory Related Fields , vol.110 , pp. 427-439
    • Marton, K.1
  • 16
    • 84974004014 scopus 로고
    • Existence and uniqueness of monotone measure preserving maps
    • MCCANN, R. (1995). Existence and uniqueness of monotone measure preserving maps. Duke Math. J. 80 309-323.
    • (1995) Duke Math. J. , vol.80 , pp. 309-323
    • Mccann, R.1
  • 17
    • 0001559554 scopus 로고    scopus 로고
    • Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
    • OTTO, F. and VILLANI, C. (2000). Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173 361-400.
    • (2000) J. Funct. Anal. , vol.173 , pp. 361-400
    • Otto, F.1    Villani, C.2
  • 18
    • 0030551055 scopus 로고    scopus 로고
    • Transportation cost for Gaussian and other product measures
    • TALAGRAND, M. (1996). Transportation cost for Gaussian and other product measures. Geom. Funct. Anal. 6 587-600.
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 587-600
    • Talagrand, M.1
  • 20
    • 0033453068 scopus 로고    scopus 로고
    • The log-Sobolev inequality for weakly coupled lattice fields
    • YOSHIDA, N. (1999a). The log-Sobolev inequality for weakly coupled lattice fields. Probab. Theory Related Fields 115 1-10.
    • (1999) Probab. Theory Related Fields , vol.115 , pp. 1-10
    • Yoshida, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.