3 citations · 6 across the 4 of their papers we have counts for
11 papers
Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds
Matthias Erbar, Chiara Rigoni, Karl-Theodor Sturm +1
We develop the theory of tamed spaces which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature and investigate these from an Eulerian point of view.…
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
Matthias Erbar, Max Fathi, André Schlichting
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics bas…
The one-dimensional log-gas free energy has a unique minimiser
Matthias Erbar, Martin Huesmann, Thomas Leblé
We prove that, at every positive temperature, the infinite-volume free energy of the one dimensional log-gas, or beta-ensemble, has a unique minimiser, which is the Sine-beta proce…
On the geometry of geodesics in discrete optimal transport
Matthias Erbar, Jan Maas, Melchior Wirth
We consider the space of probability measures on a discrete set , endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset $Y \sub…
Super Ricci flows for weighted graphs
Matthias Erbar, Eva Kopfer
We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying…
Rigidity of cones with bounded Ricci curvature
Matthias Erbar, Karl-Theodor Sturm
We show that the only metric measure space with the structure of an -cone and with two-sided synthetic Ricci bounds is the Euclidean space for integer. T…