메뉴 건너뛰기




Volumn 139, Issue 3-4, 2007, Pages 563-603

Weak logarithmic Sobolev inequalities and entropic convergence

Author keywords

Concentration inequalities; Entropy; Logarithmic Sobolev inequalities

Indexed keywords


EID: 34547217629     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0054-5     Document Type: Article
Times cited : (30)

References (31)
  • 2
    • 33846169811 scopus 로고    scopus 로고
    • Concentration for independent random variables with heavy tails
    • 2
    • Barthe F., Cattiaux P. and Roberto C. (2005). Concentration for independent random variables with heavy tails. AMRX 2005(2): 39-60
    • (2005) AMRX , vol.2005 , pp. 39-60
    • Barthe, F.1    Cattiaux, P.2    Roberto, C.3
  • 3
    • 34147152743 scopus 로고    scopus 로고
    • Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
    • Barthe F., Cattiaux P. and Roberto C. (2006). Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. Rev. Math. Iberoamericana. 22: 993-1066
    • (2006) Rev. Math. Iberoamericana. , vol.22 , pp. 993-1066
    • Barthe, F.1    Cattiaux, P.2    Roberto, C.3
  • 5
    • 84966220156 scopus 로고
    • A generalized Poincaré inequality for Gaussian measures
    • 2
    • Beckner W. (1989). A generalized Poincaré inequality for Gaussian measures. Proc. Am. Math. Soc. 105(2): 397-400
    • (1989) Proc. Am. Math. Soc. , vol.105 , pp. 397-400
    • Beckner, W.1
  • 6
    • 0348234223 scopus 로고    scopus 로고
    • Sobolev inequalities for probability measures on the real line
    • Barthe, F., Roberto, C.: Sobolev inequalities for probability measures on the real line. Studia Math. 159(3), (2003)
    • (2003) Studia Math. , vol.159 , Issue.3
    • Barthe, F.1    Roberto, C.2
  • 7
    • 0000720752 scopus 로고
    • A note on the isoperimetric constant
    • Buser P. (1982). A note on the isoperimetric constant. Ann. Sci. École Norm. Sup. 15: 213-230
    • (1982) Ann. Sci. École Norm. Sup. , vol.15 , pp. 213-230
    • Buser, P.1
  • 8
    • 0000140877 scopus 로고    scopus 로고
    • Coercive inequalities for Gibbs measures
    • 2
    • Bertini L. and Zegarlinski B. (1999). Coercive inequalities for Gibbs measures. J. Funct. Anal. 162(2): 257-286
    • (1999) J. Funct. Anal. , vol.162 , pp. 257-286
    • Bertini, L.1    Zegarlinski, B.2
  • 10
    • 0000273265 scopus 로고
    • Superadditivity of Fisher's information and Logarithmic Sobolev inequalities
    • Carlen E. (1991). Superadditivity of Fisher's information and Logarithmic Sobolev inequalities. J. Func. Anal. 101: 194-211
    • (1991) J. Func. Anal. , vol.101 , pp. 194-211
    • Carlen, E.1
  • 11
    • 3943055444 scopus 로고    scopus 로고
    • A pathwise approach of some classical inequalities
    • Cattiaux P. (2004). A pathwise approach of some classical inequalities. Potential Anal. 20: 361-394
    • (2004) Potential Anal. , vol.20 , pp. 361-394
    • Cattiaux, P.1
  • 12
    • 31644434253 scopus 로고    scopus 로고
    • Hypercontractivity for perturbed diffusion semigroups
    • 4
    • Cattiaux P. (2005). Hypercontractivity for perturbed diffusion semigroups. Ann. Fac. Sci. Toulouse Math. (6) 14(4): 609-628
    • (2005) Ann. Fac. Sci. Toulouse Math. (6) , vol.14 , pp. 609-628
    • Cattiaux, P.1
  • 13
    • 34547230796 scopus 로고    scopus 로고
    • Deviation bounds for additive functionals of Markov processes
    • to appear
    • Cattiaux, P., Guillin, A.: Deviation bounds for additive functionals of Markov processes. ESAIM Probab. Stat. (2006) (to appear)
    • (2006) ESAIM Probab. Stat.
    • Cattiaux, P.1    Guillin, A.2
  • 14
    • 33748872894 scopus 로고    scopus 로고
    • On quadratic transportation cost inequalities
    • 4
    • Cattiaux P. and Guillin A. (2006). On quadratic transportation cost inequalities. J. Math. Pures Appl. 88(4): 341-361
    • (2006) J. Math. Pures Appl. , vol.88 , pp. 341-361
    • Cattiaux, P.1    Guillin, A.2
  • 15
    • 17744364115 scopus 로고    scopus 로고
    • Capacitary criteria for Poincaré-type inequalities
    • 4
    • Chen M.F. (2005). Capacitary criteria for Poincaré-type inequalities. Potential Anal. 23(4): 303-322
    • (2005) Potential Anal. , vol.23 , pp. 303-322
    • Chen, M.F.1
  • 16
    • 26444510189 scopus 로고    scopus 로고
    • Modified logarithmic sobolev inequalities and transportation inequalities
    • 3
    • Gentil I., Guillin A. and Miclo L. (2005). Modified logarithmic sobolev inequalities and transportation inequalities. Probab. Theory Related Fields 133(3): 409-436
    • (2005) Probab. Theory Related Fields , vol.133 , pp. 409-436
    • Gentil, I.1    Guillin, A.2    Miclo, L.3
  • 17
    • 34547140720 scopus 로고    scopus 로고
    • Modified logarithmic sobolev inequalities in null curvature
    • 1
    • Gentil I., Guillin A. and Miclo L. (2007). Modified logarithmic sobolev inequalities in null curvature. Rev. Math. Iber. 23(1): 237-260
    • (2007) Rev. Math. Iber. , vol.23 , pp. 237-260
    • Gentil, I.1    Guillin, A.2    Miclo, L.3
  • 19
    • 0000575981 scopus 로고    scopus 로고
    • Isoperimetric inequalities and capacities on Riemannian manifolds
    • The Maz' ya anniversary collection, Vol. 1 (Rostock, 1998) Birkhäuser, Basel
    • Grigor'yan, A.: Isoperimetric inequalities and capacities on Riemannian manifolds. In: The Maz' ya anniversary collection, Vol. 1 (Rostock, 1998), volume 109 of Oper. Theory Adv. Appl. pp. 139-153. Birkhäuser, Basel (1999)
    • (1999) Oper. Theory Adv. Appl. , vol.109 , pp. 139-153
    • Grigor'yan, A.1
  • 20
    • 0036109823 scopus 로고    scopus 로고
    • Functional inequalities for uniformly integrable semigroups and applications to essential spectrums
    • Gong F.Z. and Wang F.Y. (2002). Functional inequalities for uniformly integrable semigroups and applications to essential spectrums. Forum Math. 14: 293-313
    • (2002) Forum Math. , vol.14 , pp. 293-313
    • Gong, F.Z.1    Wang, F.Y.2
  • 21
    • 0001464498 scopus 로고
    • 2 rates of convergence for attractive reversible nearest particle systems: The critical case
    • 3
    • 2 rates of convergence for attractive reversible nearest particle systems: the critical case. Ann. Probab. 19(3): 935-959
    • (1991) Ann. Probab. , vol.19 , pp. 935-959
    • Liggett, T.M.1
  • 22
    • 0038722404 scopus 로고    scopus 로고
    • Between Sobolev and Poincaré. in geometric aspects of Functional Analysis
    • Latała R. and Oleszkiewicz K. (2000). Between Sobolev and Poincaré. in geometric aspects of Functional Analysis. Lect. Notes Math. 1745: 147-168
    • (2000) Lect. Notes Math. , vol.1745 , pp. 147-168
    • Latała, R.1    Oleszkiewicz, K.2
  • 23
    • 0003796632 scopus 로고
    • Sobolev spaces
    • Springer, Berlin Translated from the Russian by T. O. Shaposhnikova
    • Maz'ja, V.G.: Sobolev spaces. Springer Series in Soviet Mathematics. Springer, Berlin, 1985. Translated from the Russian by T. O. Shaposhnikova
    • (1985) Springer Series in Soviet Mathematics
    • Maz'ja, V.G.1
  • 24
    • 84968476227 scopus 로고
    • Sobolev inequalities for weight spaces and supercontractivity
    • Rosen J. (1976). Sobolev inequalities for weight spaces and supercontractivity. Trans. Amer. Math. Soc. 222: 367-376
    • (1976) Trans. Amer. Math. Soc. , vol.222 , pp. 367-376
    • Rosen, J.1
  • 26
    • 0035485240 scopus 로고    scopus 로고
    • 2-convergence rates of Markov semigroups
    • 2
    • 2-convergence rates of Markov semigroups. J. Funct. Anal. 185(2): 564-603
    • (2001) J. Funct. Anal. , vol.185 , pp. 564-603
    • Röckner, M.1    Wang, F.Y.2
  • 27
    • 0002749217 scopus 로고    scopus 로고
    • Existence of the spectral gap for elliptic operators
    • 3
    • Wang F.Y. (1999). Existence of the spectral gap for elliptic operators. Arkiv Mat. 37(3): 395-407
    • (1999) Arkiv Mat. , vol.37 , pp. 395-407
    • Wang, F.Y.1
  • 28
    • 0000593993 scopus 로고    scopus 로고
    • Functional inequalities for empty essential spectrum
    • 1
    • Wang F.Y. (2000). Functional inequalities for empty essential spectrum. J. Funct. Anal. 170(1): 219-245
    • (2000) J. Funct. Anal. , vol.170 , pp. 219-245
    • Wang, F.Y.1
  • 29
    • 15244346368 scopus 로고    scopus 로고
    • A generalization of Poincaré and log-Sobolev inequalities
    • 1
    • Wang F.Y. (2005). A generalization of Poincaré and log-Sobolev inequalities. Potential Anal. 22(1): 1-15
    • (2005) Potential Anal. , vol.22 , pp. 1-15
    • Wang, F.Y.1
  • 30
    • 0035924633 scopus 로고    scopus 로고
    • Entropy bounds for Gibbs measures with non-Gaussian tails
    • 2
    • Zegarlinski B. (2001). Entropy bounds for Gibbs measures with non-Gaussian tails. J. Funct. Anal. 187(2): 368-395
    • (2001) J. Funct. Anal. , vol.187 , pp. 368-395
    • Zegarlinski, B.1
  • 31
    • 34547156230 scopus 로고    scopus 로고
    • Ph. D. Thesis. Université Paris 10
    • Zitt, P.A.: Ph. D. Thesis. Université Paris 10, 2006
    • (2006)
    • Zitt, P.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.