Matthias Erbar

erbar@math.uni-bielefeld.de
PEVZ-ID
214972424

25 Publikationen

Alle markieren

  • [25]
    2025 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980770 OA
    Burger, M., Erbar, M., Hoffmann, F., Matthes, D., & Schlichting, A. (2025). Covariance-modulated optimal transport and gradient flows. Archive for Rational Mechanics and Analysis , 249(1), 7. https://doi.org/10.1007/s00205-024-02065-w
    PUB | PDF | DOI | WoS | arXiv
     
  • [24]
    2024 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980769
    Erbar, M., Justiniano, J., & Rumpf, M. (2024). Approximation of splines in Wasserstein spaces. ESAIM:Control, Optimisation and Calculus of Variations , 30, 64. https://doi.org/10.1051/cocv/2024008
    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(11), 4441–4490. https://doi.org/10.4171/JEMS/1349
    PUB | DOI | WoS
     
  • [22]
    2023 | Preprint | PUB-ID: 2980768
    Erbar, M., Huesmann, M., Jalowy, J., & 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., & 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(5), 687-717. https://doi.org/10.3934/nhm.2022023
    PUB | DOI | Download (ext.) | WoS
     
  • [20]
    2022 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980844
    Erbar, M., Rigoni, C., Sturm, K. - T., & Tamanini, L. (2022). Tamed spaces – Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées, 161, 1-69. https://doi.org/10.1016/j.matpur.2022.02.002
    PUB | DOI | Download (ext.) | WoS
     
  • [19]
    2021 | Zeitschriftenaufsatz | PUB-ID: 2980854 OA
    Erbar, M., Huesmann, M., & Leblé, T. (2021). The one-dimensional log-gas free energy has a unique minimizer. Comm. Pure Appl. Math., 74(3), 615-675. https://doi.org/10.1002/cpa.21977
    PUB | PDF | DOI | Download (ext.)
     
  • [18]
    2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980840 OA
    Erbar, M., & Sturm, K. - T. (2021). Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS), 23(1), 219-235. https://doi.org/10.4171/jems/1010
    PUB | PDF | DOI | Download (ext.) | WoS
     
  • [17]
    2020 | Zeitschriftenaufsatz | PUB-ID: 2980838
    Erbar, M., Fathi, M., & Schlichting, A. (2020). Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA Lat. Am. J. Probab. Math. Stat., 17(1), 445-471. https://doi.org/10.30757/alea.v17-18
    PUB | DOI
     
  • [16]
    2020 | Zeitschriftenaufsatz | PUB-ID: 2980839
    Erbar, M., & Kopfer, E. (2020). Super Ricci flows for weighted graphs. J. Funct. Anal., 279(6), 108607. https://doi.org/10.1016/j.jfa.2020.108607
    PUB | DOI | WoS
     
  • [15]
    2020 | Zeitschriftenaufsatz | PUB-ID: 2980841
    Erbar, M., Rumpf, M., Schmitzer, B., & Simon, S. (2020). Computation of optimal transport on discrete metric measure spaces. Numer. Math., 144(1), 157-200. https://doi.org/10.1007/s00211-019-01077-z
    PUB | DOI
     
  • [14]
    2019 | Zeitschriftenaufsatz | PUB-ID: 2980843
    Erbar, M., Maas, J., & Wirth, M. (2019). On the geometry of geodesics in discrete optimal transport. Calc. Var. Partial Differential Equations, 58(1), Paper No. 19, 19. https://doi.org/10.1007/s00526-018-1456-1
    PUB | DOI
     
  • [13]
    2018 | Zeitschriftenaufsatz | PUB-ID: 2980849
    Erbar, M., & Fathi, M. (2018). Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature. J. Funct. Anal., 274(11), 3056-3089. https://doi.org/10.1016/j.jfa.2018.03.011
    PUB | DOI
     
  • [12]
    2018 | Zeitschriftenaufsatz | PUB-ID: 2980842
    Erbar, M., & Juillet, N. (2018). Smoothing and non-smoothing via a flow tangent to the Ricci flow. J. Math. Pures Appl. (9), 110, 123-154. https://doi.org/10.1016/j.matpur.2017.07.006
    PUB | DOI
     
  • [11]
    2017 | Zeitschriftenaufsatz | PUB-ID: 2980845
    Erbar, M., Henderson, C., Menz, G., & Tetali, P. (2017). Ricci curvature bounds for weakly interacting Markov chains. Electron. J. Probab., 22, Paper No. 40, 23. https://doi.org/10.1214/17-EJP49
    PUB | DOI
     
  • [10]
    2016 | Zeitschriftenaufsatz | PUB-ID: 2980857
    Erbar, M., Fathi, M., Laschos, V., & Schlichting, A. (2016). Gradient flow structure for McKean-Vlasov equations on discrete spaces. Discrete Contin. Dyn. Syst., 36(12), 6799-6833. https://doi.org/10.3934/dcds.2016096
    PUB | DOI
     
  • [9]
    2016 | Zeitschriftenaufsatz | PUB-ID: 2980846
    Ambrosio, L., Erbar, M., & Savar\'{e}, G. (2016). Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal., 137, 77-134. https://doi.org/10.1016/j.na.2015.12.006
    PUB | DOI
     
  • [8]
    2015 | Zeitschriftenaufsatz | PUB-ID: 2980853
    Erbar, M., Maas, J., & Renger, D. R. M. (2015). From large deviations to Wasserstein gradient flows in multiple dimensions. Electron. Commun. Probab., 20, no. 89, 12. https://doi.org/10.1214/ECP.v20-4315
    PUB | DOI
     
  • [7]
    2015 | Zeitschriftenaufsatz | PUB-ID: 2980851
    Erbar, M., Maas, J., & Tetali, P. (2015). Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models. Ann. Fac. Sci. Toulouse Math. (6), 24(4), 781-800. https://doi.org/10.5802/afst.1464
    PUB | DOI
     
  • [6]
    2015 | Zeitschriftenaufsatz | PUB-ID: 2980837
    Erbar, M., & Huesmann, M. (2015). Curvature bounds for configuration spaces. Calc. Var. Partial Differential Equations, 54(1), 397-430. https://doi.org/10.1007/s00526-014-0790-1
    PUB | DOI
     
  • [5]
    2015 | Zeitschriftenaufsatz | PUB-ID: 2980836
    Erbar, M., Kuwada, K., & Sturm, K. - T. (2015). On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces. Invent. Math., 201(3), 993-1071. https://doi.org/10.1007/s00222-014-0563-7
    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(3), 920-945. https://doi.org/10.1214/12-AIHP537
    PUB | DOI
     
  • [3]
    2014 | Zeitschriftenaufsatz | PUB-ID: 2980850
    Erbar, M., & Maas, J. (2014). Gradient flow structures for discrete porous medium equations. Discrete Contin. Dyn. Syst., 34(4), 1355-1374. https://doi.org/10.3934/dcds.2014.34.1355
    PUB | DOI
     
  • [2]
    2012 | Zeitschriftenaufsatz | PUB-ID: 2980852
    Erbar, M., & Maas, J. (2012). Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal., 206(3), 997-1038. https://doi.org/10.1007/s00205-012-0554-z
    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), 1-23. https://doi.org/10.1214/08-AIHP306
    PUB | DOI
     
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