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Distribution's template estimate with Wasserstein metrics

TLDR
Using barycenters of measures in the Wasserstein space, an iterative version as an estimation of the mean distribution is proposed, when the distributions are a common measure warped by a centered random operator, then the barycenter enables to recover this distribution template.
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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 measure…
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On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

TLDR
It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases, notably highlighted in the example of infinite-dimensional Gaussian measures.
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Trail formation based on directed pheromone deposition

TLDR
It is observed that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level, and the existence of a phase transition as the ant–pheromone interaction frequency is increased can be evidenced.
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"Exact" deviations in Wasserstein distance for empirical and occupation measures

Diffusivity of a random walk on random walks

TLDR
This paper shows 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.
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A PUNCTURED DOMAIN.

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 the…

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 mainly…
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2 Barycenters in the Wasserstein space : Notations and general results

TLDR
Using barycenters of measures in the Wasserstein space, an iterative version as an estimation of the mean distribution is proposed, when the distributions are a common measure warped by a centered random operator, then the barycenter enables to recover this distribution template.

SOME RECENT DEVELOPMENTS IN FUNCTIONAL INEQUALITIES

This paper presents different recent directions in the study of some classical functional inequalities: the Poincare inequality, the logarithmic Sobolev inequality and Talagrand's quadratic…
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