4 papers
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…
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…
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…
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…