On Some Inequalities for Gaussian Measures

By R. Lata. 2002

60 citations recorded by the source corpus.

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Citations in the corpus

On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities (2015, background): “It is interesting to note that the case (c) is related to the B-conjecture for Gaussian measures proposed by Banaszczyk (see [19]) and solved by Cordero-Erausquin, Fradelizi, and Maurey (see [8]).”
Gaussian Brunn-Minkowski inequalities (2010, background): “(Note that what Borell in [5] calls the Brunn-Minkowski inequality for Gauss measure is none of the above inequalities but is rather an isoperimetric inequality that follows from (5); see [22].”
Remarks on the conjectured log-Brunn–Minkowski inequality (2013, result): “This result is known as the (B)-Theorem (conjectured by Banaszczyk, see [8]).”
More on logarithmic sums of convex bodies (2014, background): “This was previously conjectured by Banaszczyk in [29] for the standard Gaussian measure γn (i.”
Log-Concavity and Strong Log-Concavity: a review (2014, background): “It was proved independently by a number of mathematicians at about the same time: these include Prékopa (1971, 1973), building on Borell (1974, 1975); Brascamp and Lieb (1974, 1975, 1976); Dinghas (1957), and Rinott (1976).”
The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems (2004, background): “holds for every a, b > 0? Using a deep result of LataÃla and Oleszkiewicz [13] on the rate of growth of the Gaussian measure of dilates of symmetric convex sets, LataÃla [14] noticed that (1) holds if γ(aK), γ(bK) ≥ 0.”