Some remarks on isoperimetry of Gaussian type

By L. Annalesde, ’. H. P. S. B. F. B. Arthe, B. M. Aurey. 2000

80 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/92b773923b69abea465cd77d42711e5b9947766e

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In Applied Mathematics

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Citations in the corpus

A two-sided estimate for the Gaussian noise stability deficit (2013, background): “is quite large and (ii) that B(T ) is not too close to zero when we reach 1 and thus the integrandwill be non-negligible in the (rather large) interval [ 1, 2].”
Pointwise symmetrization inequalities for Sobolev functions and applications (2009, methodology): “ α=? of the logarithm. To resolve this question, we ﬁrst need to understand the “correct” power of the logarithm that is needed here. For this we consider the isoperimetry of Qn.It is known that (cf. [15], [110, Theorem 7]) IQn ≥ Iγ. Therefore, since (Rn,γn) is of Hardy isoperimetric type (cf. [86])”
On Some Inequalities for Gaussian Measures (2002, background): “Maurey [1] gave interesting characterization of all absolutely continuous measures that satisfy Bobkov’s inequality.”
On the role of convexity in functional and isoperimetric inequalities (2008, methodology): “This has been later refined by Beckner (see [33]) using an equivalent functional form of the Gaussian isoperimetric inequality due to Bobkov [13, 14] (see also [9]): DLS2 DGau/ √ 2.”
On the isoperimetric deficit in Gauss space (2011, background): “3) has subsequently been recovered via different proofs, of probabilistic [2], [4], [18], [3] or geometric [10], [11], [12] nature.”
On the role of convexity in isoperimetry, spectral gap and concentration (2007, background): “[25]) and the unit cube K = [−1/2, 1/2]n (Hadwiger [43], see also [21],[9]).”