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math.PR2019
Bi-log-concavity: some properties and some remarks towards a multi-dimensional extension
Adrien Saumard
Bi-log-concavity of probability measures is a univariate extension of the notion of log-concavity that has been recently proposed in a statistical literature. Among other things, i…
math.PR2018
An extremal property of the normal distribution, with a discrete analog
Erwan Hillion, Oliver Johnson, Adrien Saumard
We prove, using the Brascamp-Lieb inequality, that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matri…
math.PR2018
Weighted Poincaré inequalities, concentration inequalities and tail bounds related to the Stein kernels in dimension one
Adrien Saumard
We investigate links between the so-called Stein's density approach in dimension one and some functional and concentration inequalities. We show that measures having a finite first…