no. 3
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. 
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     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},
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     url = {http://archive.numdam.org/item/AFST_2001_6_10_3_393_0/}
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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] Bakry (D.) and Ledoux (M.). - Lévy-Gromov isoperimetric inequality for an infinite dimensional diffusion generator. Invent. Math., 123:259-281, 1996. | MR 1374200 | Zbl 0855.58011

[2] Bandle (C.). - Isoperimetric inequalities and applications. Number 7 in Monographs and Studies in Math. Pitman, 1980. | MR 572958 | Zbl 0436.35063

[3] Barthe (F.) and Maurey (B.). - 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

[4] Beckner (W.). - A generalized Poincaré inequality for Gaussian measures. Proc. Amer. Math. Soc., 105:397-400, 1989. | MR 954373 | Zbl 0677.42020

[5] Blower (G.). - The Gaussian isoperimetric inequality and transportation. Preprint, 1999. | MR 2018596

[6] Bobkov (S.G.). - Extremal properties of half-spaces for log-concave distributions. Ann. Probab., 24(1):35-48, 1996. | MR 1387625 | Zbl 0859.60048

[7] Bobkov (S.G.). - Isoperimetric and analytic inequalities for log-concave probability measures. Ann. Probab., 27(4):1903-1921, 1999. | MR 1742893 | Zbl 0964.60013

[8] Bobkov (S.G.) and Houdré (C.). - Isoperimetric constants for product probability measures. Ann. Probab., 25(1):184-205, 1997. | MR 1428505 | Zbl 0878.60013

[9] Borell (C.). - Convex measures on locally convex spaces. Ark. Math., 12:239-252, 1974. | MR 388475 | Zbl 0297.60004

[10] Borell (C.). - Convex functions in d-space. Period. Math. Hungar., 6:111-136, 1975. | MR 404559 | Zbl 0274.28009

[11] Ehrhard (A.). - 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] Federer (H.). - Geometric Measure Theory. Springer-Verlag, New York, 1969. | MR 257325 | Zbl 0176.00801

[13] Ibragimov (I.A.), Sudakov (V.N.) and Tsirel'Son (B.S.). - 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

[14] Ilias (S.). - 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] Latała (R.) and Oleszkiewicz (K.). - 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

[16] Ledoux (M.). - On Talagrand's deviation inequalities for product measures. ESAIM Prob. & Stat., 1:63-87, 1996. | Numdam | Zbl 0869.60013

[17] Ledoux (M.). - 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] Pisier (G.). - 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] Polya (G.) and Szegö (G.). - Isoperimetric inequalities in mathematical physics. Princeton University Press, Princeton, 1951. | MR 43486 | Zbl 0044.38301

[20] Talagrand (M.). - 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] Wang (F.-Y.). - Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Proba. Theory Relat. Fields, 109:417-424, 1997. | MR 1481127 | Zbl 0887.35012