@article{AFST_2001_6_10_3_393_0, author = {Barthe, Franck}, title = {Levels of concentration between exponential and {Gaussian}}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {393--404}, publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences}, address = {Toulouse}, volume = {Ser. 6, 10}, number = {3}, year = {2001}, zbl = {1008.60007}, mrnumber = {1923685}, language = {en}, url = {http://archive.numdam.org/item/AFST_2001_6_10_3_393_0/} }
TY - JOUR AU - Barthe, Franck TI - Levels of concentration between exponential and Gaussian JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2001 DA - 2001/// SP - 393 EP - 404 VL - Ser. 6, 10 IS - 3 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - http://archive.numdam.org/item/AFST_2001_6_10_3_393_0/ UR - https://zbmath.org/?q=an%3A1008.60007 UR - https://www.ams.org/mathscinet-getitem?mr=1923685 LA - en ID - AFST_2001_6_10_3_393_0 ER -
Barthe, Franck. Levels of concentration between exponential and Gaussian. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 10 (2001) no. 3, pp. 393-404. http://archive.numdam.org/item/AFST_2001_6_10_3_393_0/
[1] Lévy-Gromov isoperimetric inequality for an infinite dimensional diffusion generator. Invent. Math., 123:259-281, 1996. | MR 1374200 | Zbl 0855.58011
) and ). -[2] Isoperimetric inequalities and applications. Number 7 in Monographs and Studies in Math. Pitman, 1980. | MR 572958 | Zbl 0436.35063
). -[3] Somes remarks on isoperimetry of Gaussian type. Ann. Inst. H. Poincaré, Probabilités et statistiques, 36(4):419-434, 2000. | Numdam | MR 1785389 | Zbl 0964.60018
) and ). -[4] A generalized Poincaré inequality for Gaussian measures. Proc. Amer. Math. Soc., 105:397-400, 1989. | MR 954373 | Zbl 0677.42020
). -[5] The Gaussian isoperimetric inequality and transportation. Preprint, 1999. | MR 2018596
). -[6] Extremal properties of half-spaces for log-concave distributions. Ann. Probab., 24(1):35-48, 1996. | MR 1387625 | Zbl 0859.60048
). -[7] Isoperimetric and analytic inequalities for log-concave probability measures. Ann. Probab., 27(4):1903-1921, 1999. | MR 1742893 | Zbl 0964.60013
). -[8] Isoperimetric constants for product probability measures. Ann. Probab., 25(1):184-205, 1997. | MR 1428505 | Zbl 0878.60013
) and ). -[9] Convex measures on locally convex spaces. Ark. Math., 12:239-252, 1974. | MR 388475 | Zbl 0297.60004
). -[10] Convex functions in d-space. Period. Math. Hungar., 6:111-136, 1975. | MR 404559 | Zbl 0274.28009
). -[11] Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes. Ann. Sci. Éc. Norm. Sup., 4e série, 17:317-332, 1984. | Numdam | MR 760680 | Zbl 0546.49020
). -[12] Geometric Measure Theory. Springer-Verlag, New York, 1969. | MR 257325 | Zbl 0176.00801
). -[13] Norms of Gaussian sample functions. In Proc. of the third Japan- USSR Symposium on Probability Theory, number 550 in LMN, pages 20-41. Springer, 1976. | MR 458556 | Zbl 0359.60019
), ) and ). -[14] Constantes explicites dans les inégalités de Sobolev sur les variétés riemanniennes compactes. Ann. Inst. Fourier, Grenoble, 33(2):151-165, 1983. | Numdam | MR 699492 | Zbl 0528.53040
). -[15] Between Sobolev and Poincaré. In Geometric aspects of functional analysis, volume 1745 of Lecture Notes in Math., pages 147-168. Springer, Berlin, 2000. | MR 1796718 | Zbl 0986.60017
) and ). -[16] On Talagrand's deviation inequalities for product measures. ESAIM Prob. & Stat., 1:63-87, 1996. | Numdam | Zbl 0869.60013
). -[17] Concentration of measure and logarithmic Sobolev inequalities. In Séminaire de Probabilités, XXXIII, number 1709 in Lecture Notes in Math., pages 120-216. Springer, Berlin, 1999. | Numdam | MR 1767995 | Zbl 0957.60016
). -[18] Probabilistic methods in the geometry of Banach spaces. In Probability and Analysis, Varenna (Italy) 1985, volume 1206 of Lecture Notes in Math., pages 167-241. Springer-Verlag, 1986. | MR 864714 | Zbl 0606.60008
). -[19] Isoperimetric inequalities in mathematical physics. Princeton University Press, Princeton, 1951. | MR 43486 | Zbl 0044.38301
) and ). -[20] Concentration of measure and isoerimetric inequalities in product spaces. Publications Mathématiques de l'I.H.E.S., 81:73-205, 1995. | Numdam | MR 1361756 | Zbl 0864.60013
). -[21] Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Proba. Theory Relat. Fields, 109:417-424, 1997. | MR 1481127 | Zbl 0887.35012
). -