Open Access
Volume 23, 2019
Page(s) 979 - 990
Published online 03 January 2020
  1. D. Bakry, I. Gentil and M. Ledoux, Analysis and geometry of Markov diffusion operators. In vol. 348 of Grundlehren der Mathematischen Wissenschaften (2014). [Google Scholar]
  2. S. Bobkov, Isoperimetric and analytic inequalities for log-concave probability measures. Ann. Prob. 27 (1999) 1903–1921. [Google Scholar]
  3. M. Bonnefont and A. Joulin, Intertwining relations for one-dimensional diffusions and application to functional inequalities. Potent. Anal. 41 (2014) 1005–1031. [CrossRef] [Google Scholar]
  4. M. Bonnefont, A. Joulin and Y. Ma, A note on spectral gap and weighted Poincaré inequalities for some one-dimensional diffusions. ESAIM: PS 20 (2016) 18–29. [CrossRef] [EDP Sciences] [Google Scholar]
  5. S. Boucheron and M. Thomas, Concentration inequalities for order statistics. Electr. Commun. Probab. 17 (2012) 51. [Google Scholar]
  6. T. Boucheron, G. Lugosi and P. Massart, Concentration inequalities: a nonasymptotic theory of independance. Oxford University Press (2013). [CrossRef] [Google Scholar]
  7. S. Chatterjee, Superconcentration and related topics. Springer (2014). [CrossRef] [Google Scholar]
  8. D. Cordero-Erausquin and M. Ledoux, Hypercontractive Measures Talagrand’s inequality, and Influences. Geometric aspects of functional analysis. Vol. 2050 of Lect. Notes Math. (2012) 169–189. [CrossRef] [Google Scholar]
  9. L. Gross, Logarithmic sobolev inequalities. Am. J. Math. 97 (1975) 1061–1083. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Houdré, Remarks on deviation inequalities for functions of infinitely divisible random vecteors. Ann. Probab. 30 (2002) 1223–1237. [Google Scholar]
  11. M.R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and related properties of random sequences and processes. Springer Series in Statistics (1983). [CrossRef] [Google Scholar]
  12. M. Ledoux, The geometry of Markov diffusions operators. Ann. Fac. Sci. Toulouse Math. 9 (2000) 305–366. [CrossRef] [Google Scholar]
  13. M. Ledoux, The concentration of measure phenomenon. Vol. 89 of Mathematical Surveys and Monographs (2001). [Google Scholar]
  14. F. Malrieu and D. Talay, Concentration inequalities for Euler schemes. Monte Carlo and quasi-Monte Carlo methods 2004 (2006). [Google Scholar]
  15. G. Pagès, Functional co-monotony of processes with applications to peacocks and barrier options. Séminaire de Probabilités XLV, 2078 (2013). [Google Scholar]
  16. G. Paouris and P. Valettas, A gaussian small deviation inequality for convex functions. Ann. Probab. 46 (2018) 1141–1454. [Google Scholar]
  17. G. Paouris and P. Valettas, Variance estimates and almost euclidean structure. Adv. Geometry 19 (2019) 165–189. [CrossRef] [Google Scholar]
  18. G. Paouris, P. Valettas and J. Zinn, Random version of Dvoretzky’s Theorem in lpn. Stochast. Process. Appl. 127 (2017) 3187–3227. [CrossRef] [Google Scholar]
  19. P. Valettas, On the tightness of Gaussian concentration for convex functions. J. Anal. Math. 139 (2019) 341–367. [CrossRef] [Google Scholar]
  20. K. Tanguy, Some superconcentration inequalities for extrema of stationary gaussian processes. Stat. Probab. Lett. 106 (2015) 239–246. [Google Scholar]
  21. K. Tanguy, Quelques inégalités de superconcentration: théorie et applications (in French). Ph.D. thesis, Institute of Mathematics of Toulouse (2017). [Google Scholar]
  22. K. Tanguy, Non asymptotic variance bounds and deviation inequalities by optimal transport. Electr. J. Probab. 24 (2019) 13. [Google Scholar]
  23. N. Tien Dung, An improved bound for the gaussian concentration inequality. Preprint: arXiv:1904.03674v1 (2019). [Google Scholar]
  24. P.M. Samson, Concentration inequalities for convex functions on product spaces. Stoch. Inequalit. Appl. 56 (2003) 33–52. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.