Some remarks on isoperimetry of Gaussian type (Q1584869): Difference between revisions

The authors give a martingale proof of the Gaussian isoperimetry. This also yields \textit{S. G. Bobkov's} inequality [Ann. Probab. 25, No. 1, 206-214 (1997; Zbl 0883.60031)] for the two-point space and its extension to non-symmetric Bernoulli measures. The equivalence of different forms of Gaussian type isoperimetry is shown, which allows the authors to prove a sharp form of Bobkov's inequality for the sphere and to get isoperimetric estimates for the unit cube.