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Macroscopic modelling of crowd motion
In this work, we aim at modelling crowd motion in emergency situations. We propose a macroscopic model (where people are represented as a density) following two basic... -
A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserst...
v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into... -
A geometric study of Wasserstein spaces: Hadamard spaces
This second version contains only the first part of the preceeding one. The visibility properties of W(X) and the isometric rigidity have been split off to other articles after... -
Optimal Transport : Regularity and applications
This thesis consists in two distinct parts both related to the optimal transport theory.The first part deals with the regularity of the optimal transport map. The key... -
Regularized Discrete Optimal Transport
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A geometric study of Wasserstein spaces: an addendum on the boundary
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A Dacorogna-Moser approach to flow decomposition and minimal flow problems
submitted to the proceedings of the SMAI conference 2013 -
Sliced and Radon Wasserstein Barycenters of Measures
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Lazy random walks and optimal transport on graphs
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Synthesizing and Mixing Stationary Gaussian Texture Models
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Convexities and optimal transport problems on the Wiener space
The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe... -
Numerical solution of the Monge-Kantorovich problem by Picard iterations
We present an iterative method to numerically solve the L² Monge-Kantorovich problem. The method is based on a Picard fixed point iteration of the linearized problem.... -
Far-field reflector problem and intersection of paraboloids
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On the smoothness of the potential function in Riemannian optimal transport
Preprint (submitted 2013-08-01; revised 2014-03-05), 71 pages, to appear in Communications in Analysis and Geometry, Vol. 23, No. 1 (2015). The reference [Del03] quoted on p.63... -
Discrete optimal transport: complexity, geometry and applications
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A comparison of two dual methods for discrete optimal transport
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One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: Remarks on duality ...
This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of... -
Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-pot...
This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot-Nash...
