We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported
Abstract. Let µN be the empirical measure associated to a N-sample of a given probability distributi...
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distan...
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W...
The Wasserstein distance between two probability measures on a metric spaceis a measure of closeness...
28 pagesWe are interested in the approximation in Wasserstein distance with index $\rho\ge 1$ of a p...
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hinder...
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical...
We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence...
We provide some non-asymptotic bounds, with explicit constants, that measure the rate of convergence...
Let P be a Borel-probability on and let be a family of Borel-probabilities with finite second order ...
summary:We discuss two ways to construct standard probability measures, called push-down measures, f...
Wasserstein distances or, more generally, distances that quantify the optimal transport between prob...
The problem of quantization can be thought of as follows: given a probability distribution P and a n...
An upper bound is given for the mean square Wasserstein distance between the empirical measure of a ...
Let X be a separable, complete metric space and Pp(X) be the space of Borel probability measures wit...
Abstract. Let µN be the empirical measure associated to a N-sample of a given probability distributi...
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distan...
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W...
The Wasserstein distance between two probability measures on a metric spaceis a measure of closeness...
28 pagesWe are interested in the approximation in Wasserstein distance with index $\rho\ge 1$ of a p...
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hinder...
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical...
We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence...
We provide some non-asymptotic bounds, with explicit constants, that measure the rate of convergence...
Let P be a Borel-probability on and let be a family of Borel-probabilities with finite second order ...
summary:We discuss two ways to construct standard probability measures, called push-down measures, f...
Wasserstein distances or, more generally, distances that quantify the optimal transport between prob...
The problem of quantization can be thought of as follows: given a probability distribution P and a n...
An upper bound is given for the mean square Wasserstein distance between the empirical measure of a ...
Let X be a separable, complete metric space and Pp(X) be the space of Borel probability measures wit...
Abstract. Let µN be the empirical measure associated to a N-sample of a given probability distributi...
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distan...
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W...
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