Gaussian maximum of entropy and reversed log-Sobolev inequality

Djalil Chafaï

Séminaire de probabilités de Strasbourg (2002)

  • Volume: 36, page 194-200

How to cite


Chafaï, Djalil. "Gaussian maximum of entropy and reversed log-Sobolev inequality." Séminaire de probabilités de Strasbourg 36 (2002): 194-200. <>.

author = {Chafaï, Djalil},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {Gross logarithmic Sobolev inequality; Gaussian maximum of Shannon's entropy power; reversed Gross inequality},
language = {eng},
pages = {194-200},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Gaussian maximum of entropy and reversed log-Sobolev inequality},
url = {},
volume = {36},
year = {2002},

AU - Chafaï, Djalil
TI - Gaussian maximum of entropy and reversed log-Sobolev inequality
JO - Séminaire de probabilités de Strasbourg
PY - 2002
PB - Springer - Lecture Notes in Mathematics
VL - 36
SP - 194
EP - 200
LA - eng
KW - Gross logarithmic Sobolev inequality; Gaussian maximum of Shannon's entropy power; reversed Gross inequality
UR -
ER -


  1. 1. C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Malrieu, C. Roberto, and G. Scheffer. Sur les inégalités de Sobolev logarithmiques. with an introduction by D. Bakry and M. Ledoux, to appear in "Panoramas et Synthèses, Société Mathématique de France, 2000. Zbl0982.46026MR1845806
  2. 2. D. Bakry, D. Concordet, and M. Ledoux. Optimal heat kernel bounds under logarithmic Sobolev inequalities. ESAIM Probab. Statist., 1:391-407 (electronic), 1997. Zbl0898.58052MR1486642
  3. 3. F. Barthe, D. Cordero-Erausquin, and M. Fradelizi. Shift inequalities of gaussian type and norms of barycenters. preprint, september 1999. Zbl0984.60024MR1853445
  4. 4. W. Beckner. Geometric asymptotics and the logarithmic Sobolev inequality. Forum Math., 11(1):105-137, 1999. Zbl0917.58049MR1673903
  5. 5. N. Blachman. The convolution inequality for entropy powers. IEEE Trans. Information Theory, IT-11:267-271, 1965. Zbl0134.37401MR188004
  6. 6. S. Bobkov. The size of singular component and shift inequalities. Ann. Probab., 27:416-431, 1999. Zbl0946.60008MR1681090
  7. 7. E. Carlen. Super-additivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal., 101(1):194-211, 1991. Zbl0732.60020MR1132315
  8. 8. T. Cover and J. Thomas. Elements of information theory. John Wiley & Sons Inc., New York, 1991. A Wiley-Interscience Publication. Zbl0762.94001
  9. 9. A. Dembo. Information inequalities and uncertainty principles. In Tech. Rep., Dept. of Statist. Stanford Univ., 1990. 
  10. 10. A. Dembo, T. Cover, and J. Thomas. Information-theoretic inequalities. IEEE Trans. Inform. Theory, 37(6):1501-1518, 1991. Zbl0741.94001MR1134291
  11. 11. L. Gross. Logarithmic Sobolev inequalities. Amer. J. Math., 97(4):1061-1083, 1975. Zbl0318.46049MR420249
  12. 12. M. Ledoux. Concentration of measure and logarithmic Sobolev inequalities. In Séminaire de Probabilités, XXXIII, Lecture Notes in Math., pages 120-216. Springer, Berlin, 1999. Zbl0957.60016MR1767995
  13. 13. M. Ledoux. The geometry of Markov Diffusion Generators. Ann. Fac. Sci. Toulouse Math., IX(2):305-366, 2000. Zbl0980.60097MR1813804
  14. 14. M.S. Pinsker. Information and information stability of random variables and processes. Holden-Day Inc., San Francisco, Calif., 1964. Translated by Amiel Feinstein. Zbl0125.09202MR213190
  15. 15. C. Shannon. A mathematical theory of communication. Bell System Tech. J., 27:379-423, 623-656, 1948. Zbl1154.94303MR26286
  16. 16. A. Stam. Some inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control, 2:101-112, 1959. Zbl0085.34701MR109101

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