18 citations · 47 across the 11 of their papers we have counts for
8 papers · 1 filter
Covariance inequalities for convex and log-concave functions
Michel Bonnefont, Erwan Hillion, Adrien Saumard
Extending results of Harg{é} and Hu for the Gaussian measure, we prove inequalities for the covariance Cov where is a general product probability measure on $\mathbb{…
A proof of the Shepp-Olkin entropy monotonicity conjecture
Erwan Hillion, Oliver Johnson
Consider tossing a collection of coins, each fair or biased towards heads, and take the distribution of the total number of heads that result. It is natural to conjecture that this…
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…
A proof of the Shepp-Olkin entropy concavity conjecture
Erwan Hillion, Oliver Johnson
We prove the Shepp--Olkin conjecture, which states that the entropy of the sum of independent Bernoulli random variables is concave in the parameters of the individual random varia…
Entropy along W_{1,+}-geodesics on graphs
Erwan Hillion
We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.
-interpolation of probability measures on graphs
Erwan Hillion
We generalize an equation introduced by Benamou and Brenier, characterizing Wasserstein W_p-geodesics for p > 1, from the continuous setting of probability distributions on a Riema…
Discrete versions of the transport equation and the Shepp-Olkin conjecture
Erwan Hillion, Oliver Johnson
We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems i…
A natural derivative on [0,n] and a binomial Poincaré inequality
Erwan Hillion, Oliver Johnson, Yaming Yu
We consider probability measures supported on a finite discrete interval . We introduce a new finitedifference operator , defined as a linear combination of left a…