PUB - Publikationen an der Universität Bielefeld

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• [25]
  

  2025 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980770

  M. Burger, M. Erbar, F. Hoffmann, D. Matthes, and A. Schlichting, “Covariance-modulated optimal transport and gradient flows”, Archive for Rational Mechanics and Analysis , 2025, 249, : 7.

  PUB | PDF | DOI | WoS | arXiv
   
• [24]
  

  2024 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980769

  M. Erbar, J. Justiniano, and M. Rumpf, “Approximation of splines in Wasserstein spaces”, ESAIM:Control, Optimisation and Calculus of Variations , 2024, 30, : 64.

  PUB | DOI | WoS | arXiv
   
• [23]
  

  2023 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980771

  M. Erbar, “A gradient flow approach to the Boltzmann equation”, Journal of the European Mathematical Society (JEMS) , 2023, 26, 4441–4490.

  PUB | DOI | WoS
   
• [22]
  

  2023 | Preprint | PUB-ID: 2980768

  M. Erbar, M. Huesmann, J. Jalowy, and B. M\, “Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy”, arXiv:2304.11145, 2023.

  PUB | arXiv
   
• [21]
  

  2022 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980855

  M. Erbar, D. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph”, Networks and Heterogeneous Media: An Applied Mathematics Journal, 2022, 17, 687-717.

  PUB | DOI | Download (ext.) | WoS
   
• [20]
  

  2022 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980844

  M. Erbar, C. Rigoni, K. - T. Sturm, and L. Tamanini, “Tamed spaces – Dirichlet spaces with distribution-valued Ricci bounds”, Journal de Mathématiques Pures et Appliquées, 2022, 161, 1-69.

  PUB | DOI | Download (ext.) | WoS
   
• [19]
  

  2021 | Zeitschriftenaufsatz | PUB-ID: 2980854

  M. Erbar, M. Huesmann, and T. Leblé, “The one-dimensional log-gas free energy has a unique minimizer”, Comm. Pure Appl. Math., 2021, 74, 615-675.

  PUB | PDF | DOI | Download (ext.)
   
• [18]
  

  2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980840

  M. Erbar, and K. - T. Sturm, “Rigidity of cones with bounded Ricci curvature”, J. Eur. Math. Soc. (JEMS), 2021, 23, 219-235.

  PUB | PDF | DOI | Download (ext.) | WoS
   
• [17]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980838

  M. Erbar, M. Fathi, and A. Schlichting, “Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces”, ALEA Lat. Am. J. Probab. Math. Stat., 2020, 17, 445-471.

  PUB | DOI
   
• [16]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980839

  M. Erbar, and E. Kopfer, “Super Ricci flows for weighted graphs”, J. Funct. Anal., 2020, 279, 108607.

  PUB | DOI | WoS
   
• [15]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980841

  M. Erbar, M. Rumpf, B. Schmitzer, and S. Simon, “Computation of optimal transport on discrete metric measure spaces”, Numer. Math., 2020, 144, 157-200.

  PUB | DOI
   
• [14]
  

  2019 | Zeitschriftenaufsatz | PUB-ID: 2980843

  M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete optimal transport”, Calc. Var. Partial Differential Equations, 2019, 58, Paper No. 19, 19.

  PUB | DOI
   
• [13]
  

  2018 | Zeitschriftenaufsatz | PUB-ID: 2980849

  M. Erbar, and M. Fathi, “Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature”, J. Funct. Anal., 2018, 274, 3056-3089.

  PUB | DOI
   
• [12]
  

  2018 | Zeitschriftenaufsatz | PUB-ID: 2980842

  M. Erbar, and N. Juillet, “Smoothing and non-smoothing via a flow tangent to the Ricci flow”, J. Math. Pures Appl. (9), 2018, 110, 123-154.

  PUB | DOI
   
• [11]
  

  2017 | Zeitschriftenaufsatz | PUB-ID: 2980845

  M. Erbar, C. Henderson, G. Menz, and P. Tetali, “Ricci curvature bounds for weakly interacting Markov chains”, Electron. J. Probab., 2017, 22, Paper No. 40, 23.

  PUB | DOI
   
• [10]
  

  2016 | Zeitschriftenaufsatz | PUB-ID: 2980857

  M. Erbar, M. Fathi, V. Laschos, and A. Schlichting, “Gradient flow structure for McKean-Vlasov equations on discrete spaces”, Discrete Contin. Dyn. Syst., 2016, 36, 6799-6833.

  PUB | DOI
   
• [9]
  

  2016 | Zeitschriftenaufsatz | PUB-ID: 2980846

  L. Ambrosio, M. Erbar, and G. Savar\'{e}, “Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces”, Nonlinear Anal., 2016, 137, 77-134.

  PUB | DOI
   
• [8]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980853

  M. Erbar, J. Maas, and D. R. M. Renger, “From large deviations to Wasserstein gradient flows in multiple dimensions”, Electron. Commun. Probab., 2015, 20, no. 89, 12.

  PUB | DOI
   
• [7]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980851

  M. Erbar, J. Maas, and P. Tetali, “Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models”, Ann. Fac. Sci. Toulouse Math. (6), 2015, 24, 781-800.

  PUB | DOI
   
• [6]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980837

  M. Erbar, and M. Huesmann, “Curvature bounds for configuration spaces”, Calc. Var. Partial Differential Equations, 2015, 54, 397-430.

  PUB | DOI
   
• [5]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980836

  M. Erbar, K. Kuwada, and K. - T. Sturm, “On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces”, Invent. Math., 2015, 201, 993-1071.

  PUB | DOI
   
• [4]
  

  2014 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980848

  M. Erbar, “Gradient flows of the entropy for jump processes”, Ann. Inst. Henri Poincaré Probab. Stat., 2014, 50, 920-945.

  PUB | DOI
   
• [3]
  

  2014 | Zeitschriftenaufsatz | PUB-ID: 2980850

  M. Erbar, and J. Maas, “Gradient flow structures for discrete porous medium equations”, Discrete Contin. Dyn. Syst., 2014, 34, 1355-1374.

  PUB | DOI
   
• [2]
  

  2012 | Zeitschriftenaufsatz | PUB-ID: 2980852

  M. Erbar, and J. Maas, “Ricci curvature of finite Markov chains via convexity of the entropy”, Arch. Ration. Mech. Anal., 2012, 206, 997-1038.

  PUB | DOI
   
• [1]
  

  2010 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980858

  M. Erbar, “The heat equation on manifolds as a gradient flow in the Wasserstein space”, Annales de l'Institut Henri Poincaré (B): Probability and Statistics, 2010, 46, 1-23.

  PUB | DOI