4 papers
Wasserstein Gradient Flows of semi-discret energies: evolution of urban areas anduniform quantization
Joao Miguel Machado
We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continu…
Quantitative Stability for Minkowski's problem
Károly Böröczky, João Miguel Machado, João P. G. Ramos
We derive quantitative stability results for Minkowski bodies, as well as their counterparts, the -Minkowski bodies in the range . We prove that, for every pai…
From Nash to Cournot--Nash equilibria via -convergence
João Miguel Machado, Guilherme Mazanti, Laurent Pfeiffer
This work addresses the issue of the convergence of an -player game towards a limit model involving a continuum of players, as the number of agents goes to infinity. More pr…
Absence of loops for the Wasserstein- problem: the concentration/blow-up argument
Jo{ã}o Miguel Machado
In the present work we prove that minimizers of the Wasserstein- problem, introduced recently by Chambolle et. al., are trees in two cases: when the target measure i…