Erwan Hillion

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We consider probability measures supported on a finite discrete interval [0, n]. We introduce a new finite difference operator ∇n, defined as a linear combination of left and right finite differences. We show that this operator ∇n plays a key role in a new Poincaré (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk(More)
Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin about the entropy of sums of Bernoulli random variables, we prove the concavity in t of the entropy of the convolution of a probability measure a, which has the law of a sum of independent Bernoulli variables, by the binomial measure(More)
We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula. Further, we use these coefficients to state a new form of(More)
We generalize an equation introduced by Benamou and Brenier in [BB00] and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a final distributions (f0(x))x∈G, (f1(x))x∈G, we prove the(More)
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