1 citations · 1 across the 4 of their papers we have counts for
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On Convex Functions of Gaussian Variables
Maite Fernández-Unzueta, James Melbourne, Gerardo Palafox-Castillo
We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variab…
Rearrangements and infimum convolutions
Devraj Duggal, James Melbourne, Cyril Roberto
We develop a general comparison result for inf convolution operators related to rearrangement. As a consequence we derive comparison results under spherically symmetric rearrangeme…
Anti-concentration inequalities for log-concave variables on the real line
Tulio Gaxiola, James Melbourne, Vincent Pigno +1
We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majoriz…
Hyperbolic Measures on Infinite Dimensional Spaces
Sergey G. Bobkov, James Melbourne
Localization and dilation procedures are discussed for infinite dimensional -concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measu…