Concentration for independent random variables with heavy tails

Applied Mathematics Research eXpress

Volumn 2005, Issue , 2005, Pages 39-60

  Barthe, F ^a   Cattiaux, P ^b,c   Roberto, C ^d  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^d UNIVERSITÉ PARIS EST CRÉTEIL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846169811     PISSN: 16871200     EISSN: 16871197     Source Type: Journal    
DOI: 10.1155/amrx.2005.39     Document Type: Article

References (16)

1. S. Aida, An estimate of the gap of spectrum of Schrodinger operators which generate hyperbounded semigroups, J. Funct. Anal. 185 (2001), no. 2, 474-526.
2. S. Aida, T Masuda, and I. Shigekawa, Logarithmic Sobolev inequalities and exponential integrability, J. Funct. Anal. 126 (1994), no. 1, 83-101.
3. F. Barthe, P. Cattiaux, and C. Roberto, Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and application to isoperimetry, to appear in Rev. Mat. Iberoamericana.
4. F. Barthe and C. Roberto, Sobolev inequalities for probability measures on the real line, Studia Math. 159 (2003), no. 3, 481-497 (Polish).
5. S. G. Bobkov and C. Houdré, Some connections between isoperimetric and Sobolev-type inequalities, Mem. Amer. Math. Soc. 129 (1997), no. 616, viii+111.
6. -, Weak dimension-free concentration of measure, Bernoulli 6 (2000), no. 4, 621-632.
7. A. A. Borovkov and S. A. Utev, An inequality and a characterization of the normal distribution connected with it, Teor. Veroyatnost. i Primenen. 28 (1983), no. 2, 209-218 (Russian).
8. M. Gromov and V. D. Milman, A topological application of the isoperimetric inequality, Amer. J. Math. 105 (1983), no. 4, 843-854.
9. R. Latała and K. Oleszkiewicz, Between Sobolev and Poincaré, Geometric Aspects of Functional Analysis, Lecture Notes in Math., vol. 1745, Springer, Berlin, 2000, pp. 147-168.
10. M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probabilitiés XXXIII, Lecture Notes in Math., vol. 1709, Springer, Berlin, 1999, pp. 120-216.
11. -, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, vol. 89, American Mathematical Society, Rhode Island, 2001.
12. 2-convergence rates of Markov semigroups, J. Funct. Anal. 185 (2001), no. 2, 564-603.
13. n ball, Geometric Aspects of Functional Analysis, Lecture Notes in Math., vol. 1745, Springer, Berlin, 2000, pp. 245-256.
14. M. Talagrand, A new isoperimetric inequality and the concentration of measure phenomenon, Geometric Aspects of Functional Analysis 1989-1990 (J. Lindenstrauss and V. D. Milman, eds.), Lecture Notes in Math., vol. 1469, Springer, Berlin, 1991, pp. 94-124.
15. F.-Y. Wang, A generalization of Poincare and log-Sobolev inequalities, to appear in Potential Anal.
16. F.-Y. Wang and Q. Zhang, Weak Poincaré inequalities, decay of Markov semigroups and concentration of measure, preprint, 2005.