Matthias Erbar, Jan Maas and Melchior Wirth On the geometry of geodesics in discrete optimal transport Calc. Var. Partial Differential Equations, 58(1): Art. 19, 19 2019 10.1007/s00526-018-1456-1
Matthias Erbar and Karl-Theodor Sturm Riggidity of cones with bounded curvature to appear in JEMS, arxiv e-print 1712.08093 2019 https://arxiv.org/abs/1712.08093
2018
Matthias Erbar and Nicolas Juillet Smoothing and non-smoothing via a flow tangent to the Ricci flow J. Math. Pures Appl. (9), 110: 123--154 2018 10.1016/j.matpur.2017.07.006
Matthias Erbar, Martin Rumpf, Bernhard Schmitzer and Stefan Simon Computation of Optimal Transport on Discrete Metric Measure Spaces Unknown https://arxiv.org/abs/1707.06859
Matthias Erbar A gradient flow approach to the Boltzmann equation arxiv e-print 1603.0540 2017 https://arxiv.org/abs/1603.0540
2015
Matthias Erbar, Jan Maas and Prasad Tetali Ricci curvature bounds for Bernoulli-Laplace and random transposition models Ann. Fac. Sci. Toulouse Math., ArXiv e-prints, 24(4): 781-800 2015 http://arxiv.org/abs/1409.8605
Abstract: We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the $n$-dimensional discrete cube (the so-called Bernoulli-Laplace model) and the random transposition shuffle of the symmetric group of permutations on $n$ letters.
Matthias Erbar, Kazumasa Kuwada and Karl-Theodor Sturm On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces Invent. Math., 201(3): 993-1071 2015 http://dx.doi.org/10.1007/s00222-014-0563-7
Matthias Erbar and Martin Huesmann Curvature bounds for configuration spaces Calculus of Variations and Partial Differential Equations, 54(1): 397-430 2015 http://dx.doi.org//10.1007/s00526-014-0790-1