PUB - Publikationen an der Universität Bielefeld

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• [25]
  

  2025 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980770

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

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

  2024 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980769

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

  PUB | DOI | WoS | arXiv
   
• [23]
  

  2023 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980771

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

  PUB | DOI | WoS
   
• [22]
  

  2023 | Preprint | PUB-ID: 2980768

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

  PUB | arXiv
   
• [21]
  

  2022 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980855

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

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

  2022 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980844

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

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

  2021 | Zeitschriftenaufsatz | PUB-ID: 2980854

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

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• [18]
  

  2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980840

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

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• [17]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980838

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

  PUB | DOI
   
• [16]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980839

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

  PUB | DOI | WoS
   
• [15]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980841

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

  PUB | DOI
   
• [14]
  

  2019 | Zeitschriftenaufsatz | PUB-ID: 2980843

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

  PUB | DOI
   
• [13]
  

  2018 | Zeitschriftenaufsatz | PUB-ID: 2980849

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

  PUB | DOI
   
• [12]
  

  2018 | Zeitschriftenaufsatz | PUB-ID: 2980842

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

  PUB | DOI
   
• [11]
  

  2017 | Zeitschriftenaufsatz | PUB-ID: 2980845

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

  PUB | DOI
   
• [10]
  

  2016 | Zeitschriftenaufsatz | PUB-ID: 2980857

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

  PUB | DOI
   
• [9]
  

  2016 | Zeitschriftenaufsatz | PUB-ID: 2980846

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

  PUB | DOI
   
• [8]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980853

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

  PUB | DOI
   
• [7]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980851

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

  PUB | DOI
   
• [6]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980837

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

  PUB | DOI
   
• [5]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980836

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

  PUB | DOI
   
• [4]
  

  2014 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980848

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

  PUB | DOI
   
• [3]
  

  2014 | Zeitschriftenaufsatz | PUB-ID: 2980850

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

  PUB | DOI
   
• [2]
  

  2012 | Zeitschriftenaufsatz | PUB-ID: 2980852

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

  PUB | DOI
   
• [1]
  

  2010 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980858

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

  PUB | DOI