Gaussian maximum of entropy and reversed log-Sobolev inequality
Séminaire de probabilités de Strasbourg (2002)
- Volume: 36, page 194-200
Access Full Article
top
How to cite
topChafaï, Djalil. "Gaussian maximum of entropy and reversed log-Sobolev inequality." Séminaire de probabilités de Strasbourg 36 (2002): 194-200. <http://eudml.org/doc/114086>.
@article{Chafaï2002,
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 = {http://eudml.org/doc/114086},
volume = {36},
year = {2002},
}
TY - JOUR
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 - http://eudml.org/doc/114086
ER -
References
top- 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. 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. F. Barthe, D. Cordero-Erausquin, and M. Fradelizi. Shift inequalities of gaussian type and norms of barycenters. preprint, september 1999. Zbl0984.60024MR1853445
- 4. W. Beckner. Geometric asymptotics and the logarithmic Sobolev inequality. Forum Math., 11(1):105-137, 1999. Zbl0917.58049MR1673903
- 5. N. Blachman. The convolution inequality for entropy powers. IEEE Trans. Information Theory, IT-11:267-271, 1965. Zbl0134.37401MR188004
- 6. S. Bobkov. The size of singular component and shift inequalities. Ann. Probab., 27:416-431, 1999. Zbl0946.60008MR1681090
- 7. E. Carlen. Super-additivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal., 101(1):194-211, 1991. Zbl0732.60020MR1132315
- 8. T. Cover and J. Thomas. Elements of information theory. John Wiley & Sons Inc., New York, 1991. A Wiley-Interscience Publication. Zbl0762.94001
- 9. A. Dembo. Information inequalities and uncertainty principles. In Tech. Rep., Dept. of Statist. Stanford Univ., 1990.
- 10. A. Dembo, T. Cover, and J. Thomas. Information-theoretic inequalities. IEEE Trans. Inform. Theory, 37(6):1501-1518, 1991. Zbl0741.94001MR1134291
- 11. L. Gross. Logarithmic Sobolev inequalities. Amer. J. Math., 97(4):1061-1083, 1975. Zbl0318.46049MR420249
- 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. M. Ledoux. The geometry of Markov Diffusion Generators. Ann. Fac. Sci. Toulouse Math., IX(2):305-366, 2000. Zbl0980.60097MR1813804
- 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. C. Shannon. A mathematical theory of communication. Bell System Tech. J., 27:379-423, 623-656, 1948. Zbl1154.94303MR26286
- 16. A. Stam. Some inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control, 2:101-112, 1959. Zbl0085.34701MR109101
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.