AG Erbar

Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy
with Martin Huesmann, Jonas Jalowy, and Bastian Müller
arXiv:2304.11145, 2023. 

Covariance-modulated optimal transport and gradient flows
with Martin Burger, Franca Hoffmann, Daniel Matthes and Andre Schlichting
arXiv:2302.07773

Approximation of Splines in Wasserstein Spaces
with Jorge Justiniano and Martin Rumpf
arXiv:2302.10682

Gradient flow formulation of diffusion equations in the Wasserstein
 space over a metric graph
with Dominik Forkert, Jan Mass and Delio Mugnolo
Netw. Heterog. Media 17, no. 5, 687–717, (2022).

Tamed spaces - Dirichlet spaces with distribution-valued Ricci bounds
with Chiara Rigoni, Karl-Theodor Sturm and Luca Tamanini
J. Math. Pures Appl. (9) 161, (2022).

A gradient flow approach to the Boltzmann equation
to appear in J. Eur. Math. Soc.
arxiv:1603.0540

Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
with Max Fathi and André Schlichting
 ALEA Lat. Am. J. Probab. Math. Stat. Vol. 17, no. 1, 445--471, (2020).

Rigidity of cones with bounded Ricci curvature
with Karl-Theodor Sturm
J. Eur. Math. Soc., 23, No. 1, 219-235 (2021)

Computation of Optimal Transport on Discrete Metric Measure Spaces
with Martin Rumpf, Bernhard Schmitzer and Stefan Simon,
Numer. Math., Vol. 144, No. 1, 157--200, (2020)

Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
with Max Fathi
J. Funct. Anal., Vol. 274, No. 11, 3056-3089, (2018)

Smoothing and non-smoothing via a flow tangent to the Ricci flow
with Nicolas Juillet
J. Math. Pures Appl., Vol. 110, 123-154, (2018)

Ricci bounds for weakly interacting Markov chains
with Christopher Henderson, Georg Menz and Prasad Tetali
Electron. J. Probab. Vol. 22, No. 40, 1-23, (2017)

Gradient flow structure for McKean-Vlasov equations on discrete spaces
with Max Fathi, Vaios Laschos and Andre Schlichting
Discrete and Continuous Dynamical Systems, 36 (12), 6799--6833, (2016)

Optimal transport, Cheeger energies and contractivity
of dynamic transport distances in extended spaces
with Luigi Ambrosio and Giuseppe Savaré
Nonlinear Anal. Vol. 137, 77–134 (2016)

From large deviations to Wasserstein gradient flows in multiple dimensions
with Jan Maas and Michiel Renger
Electron. Commun. Probab. Vol. 20, No. 89, 1-12, (2015)

Ricci curvature bounds for Bernoulli-Laplace and random transposition models
with Jan Maas and Prasad Tetali
Ann. Fac. Sci. Toulouse Math. Vol. 24, No. 4, 781–800, (2015)

Curvature bounds for configuration spaces
with Martin Huesmann
Calc. Var. PDE, 201 (3), 397-430, (2014)

On the equivalence of Bochner's inequality and the entropic curvature-dimension
condition on metric measure spaces
with Kazumasa Kuwada and Karl-Theodor Sturm
Invent. math. 201 (3), 993-1071, (2015)

Gradient flow structures for discrete porous medium equations
with Jan Maas
Discrete and Continuous Dynamical Systems 34 (4), 1355-1374, (2014)

Gradient flows of the entropy for jump processes
Ann. Inst. H. Poincare Probab. Stat. 50 (3), 920-945, (2014)

Ricci curvature of finite Markov chains via convexity of the entropy
with Jan Maas
Arch. Rat. Mech. Anal. 206 (3), 997-1038, (2012)

The heat equation on manifolds as a gradient flow in the Wasserstein space
Ann. Inst. H. Poincare Probab. Stat. 46 (1), 1-23, (2010)