论文信息 - A new isoperimetric inequality and the concentration of measure phenomenon

A new isoperimetric inequality and the concentration of measure phenomenon

We prove a new isoperimetric inequality for a certain product measure that improves upon some aspects of the “large deviation” consequences of the isoperimetric inequality for the Gaussian measure.

M. Talagrand

[1] W. Hoeffding. Probability Inequalities for sums of Bounded Random Variables , 1963 .

[2] C. Borell. The Brunn-Minkowski inequality in Gauss space , 1975 .

[3] V. Sudakov,et al. Extremal properties of half-spaces for spherically invariant measures , 1978 .

[4] A. Ehrhard. Symétrisation dans l'espace de Gauss. , 1983 .

[5] A. Ehrhard. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes , 1984 .

[6] Sur l'intégrabilité des vecteurs gaussiens , 1984 .

[7] G. Pisier. Probabilistic methods in the geometry of Banach spaces , 1986 .