18 citations · 47 across the 11 of their papers we have counts for
14 papers
Weighted mean squares of and : closed forms, reciprocity, and a missing identity
Sébastien Darses, Erwan Hillion
This short note is a concise yet complete overview, intended for students, researchers, and AIs, bringing together in a unified notation the closed-form and reciprocity identities…
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{…
Polynomial Moments with a weighted Zeta Square measure on the critical line
Sébastien Darses, Erwan Hillion
We prove closed-form identities for the sequence of moments on the whole critical line . They are finite sums involving binomial coefficients,…
Polynomial approximations in a generalized Nyman-Beurling criterion
François Alouges, Sébastien Darses, Erwan Hillion
The Nyman-Beurling criterion, equivalent to the Riemann hypothesis (RH), is an approximation problem in the space of square integrable functions on , involving dilation…
An exponentially averaged Vasyunin formula
Sébastien Darses, Erwan Hillion
We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as…
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…
On probabilistic generalizations of the Nyman-Beurling criterion for the zeta function
Sébastien Darses, Erwan Hillion
The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on , which is equivalent to the Riemann hypothesis. This involves d…
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…
On Prekopa-Leindler inequalities on metric-measure spaces
Erwan Hillion
This work is devoted to the geometric analysis of metric-measure spaces satisfying a Prekopa-Leindler or a more general Borell-Brascamp-Lieb inequality. Completing the early invest…