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Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance
We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measureExpand
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Distribution's template estimate with Wasserstein metrics
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the WassersteinExpand
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Trail formation based on directed pheromone deposition
We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromone particles and interact with them through alignmentExpand
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On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measuresExpand
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Séminaire de probabilités XLIX
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Diffusivity of a random walk on random walks
We consider a random walk Zn1 with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor i¾?K2=2K+2 with respect to the case of the classical simple random walk without constraint. Expand
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Problèmes d'interaction discret-continu et distances de Wasserstein
On etudie dans ce manuscrit plusieurs problemes d'approximation a l'aide des outils de la theorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur pourExpand
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In this paper we study the Poincare constant for the Gaussian measure re- stricted to D = R d B(y,r) where B(y,r) denotes the Euclidean ball with center y and radius r, and d � 2. We also study theExpand
Ornstein-Uhlenbeck pinball and the Poincaré inequality in a punctured domain.
In this paper we study the Poincare constant for the Gaussian measure restricted to \(D={\mathbb R}^d - \mathbb {B}\) where \(\mathbb {B}\) is the disjoint union of bounded open sets. We will mainlyExpand