PUB - Publikationen an der Universität Bielefeld

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• [25]
  

  2025 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980770

  Burger, Martin, Erbar, Matthias, Hoffmann, Franca, Matthes, Daniel, and Schlichting, André. “Covariance-modulated optimal transport and gradient flows”. Archive for Rational Mechanics and Analysis 249.1 (2025): 7.

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

  2024 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980769

  Erbar, Matthias, Justiniano, Jorge, and Rumpf, Martin. “Approximation of splines in Wasserstein spaces”. ESAIM:Control, Optimisation and Calculus of Variations 30 (2024): 64.

  PUB | DOI | WoS | arXiv
   
• [23]
  

  2023 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980771

  Erbar, Matthias. “A gradient flow approach to the Boltzmann equation”. Journal of the European Mathematical Society (JEMS) 26.11 (2023): 4441–4490.

  PUB | DOI | WoS
   
• [22]
  

  2023 | Preprint | PUB-ID: 2980768

  Erbar, Matthias, Huesmann, Martin, Jalowy, Jonas, and M\, Bastian. “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

  Erbar, Matthias, Forkert, Dominik, Maas, Jan, and Mugnolo, Delio. “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph”. Networks and Heterogeneous Media: An Applied Mathematics Journal 17.5 (2022): 687-717.

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

  2022 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980844

  Erbar, Matthias, Rigoni, Chiara, Sturm, Karl-Theodor, and Tamanini, Luca. “Tamed spaces – Dirichlet spaces with distribution-valued Ricci bounds”. Journal de Mathématiques Pures et Appliquées 161 (2022): 1-69.

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

  2021 | Zeitschriftenaufsatz | PUB-ID: 2980854

  Erbar, Matthias, Huesmann, Martin, and Leblé, Thomas. “The one-dimensional log-gas free energy has a unique minimizer”. Comm. Pure Appl. Math. 74.3 (2021): 615-675.

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

  2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980840

  Erbar, Matthias, and Sturm, Karl-Theodor. “Rigidity of cones with bounded Ricci curvature”. J. Eur. Math. Soc. (JEMS) 23.1 (2021): 219-235.

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

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980838

  Erbar, Matthias, Fathi, Max, and Schlichting, Andre. “Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces”. ALEA Lat. Am. J. Probab. Math. Stat. 17.1 (2020): 445-471.

  PUB | DOI
   
• [16]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980839

  Erbar, Matthias, and Kopfer, Eva. “Super Ricci flows for weighted graphs”. J. Funct. Anal. 279.6 (2020): 108607.

  PUB | DOI | WoS
   
• [15]
  

  2020 | Zeitschriftenaufsatz | PUB-ID: 2980841

  Erbar, Matthias, Rumpf, Martin, Schmitzer, Bernhard, and Simon, Stefan. “Computation of optimal transport on discrete metric measure spaces”. Numer. Math. 144.1 (2020): 157-200.

  PUB | DOI
   
• [14]
  

  2019 | Zeitschriftenaufsatz | PUB-ID: 2980843

  Erbar, Matthias, Maas, Jan, and Wirth, Melchior. “On the geometry of geodesics in discrete optimal transport”. Calc. Var. Partial Differential Equations 58.1 (2019): Paper No. 19, 19.

  PUB | DOI
   
• [13]
  

  2018 | Zeitschriftenaufsatz | PUB-ID: 2980849

  Erbar, Matthias, and Fathi, Max. “Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature”. J. Funct. Anal. 274.11 (2018): 3056-3089.

  PUB | DOI
   
• [12]
  

  2018 | Zeitschriftenaufsatz | PUB-ID: 2980842

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

  PUB | DOI
   
• [11]
  

  2017 | Zeitschriftenaufsatz | PUB-ID: 2980845

  Erbar, Matthias, Henderson, Christopher, Menz, Georg, and Tetali, Prasad. “Ricci curvature bounds for weakly interacting Markov chains”. Electron. J. Probab. 22 (2017): Paper No. 40, 23.

  PUB | DOI
   
• [10]
  

  2016 | Zeitschriftenaufsatz | PUB-ID: 2980857

  Erbar, Matthias, Fathi, Max, Laschos, Vaios, and Schlichting, Andre. “Gradient flow structure for McKean-Vlasov equations on discrete spaces”. Discrete Contin. Dyn. Syst. 36.12 (2016): 6799-6833.

  PUB | DOI
   
• [9]
  

  2016 | Zeitschriftenaufsatz | PUB-ID: 2980846

  Ambrosio, Luigi, Erbar, Matthias, and Savar\'{e}, Giuseppe. “Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces”. Nonlinear Anal. 137 (2016): 77-134.

  PUB | DOI
   
• [8]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980853

  Erbar, Matthias, Maas, Jan, and Renger, D. R. Michiel. “From large deviations to Wasserstein gradient flows in multiple dimensions”. Electron. Commun. Probab. 20 (2015): no. 89, 12.

  PUB | DOI
   
• [7]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980851

  Erbar, Matthias, Maas, Jan, and Tetali, Prasad. “Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models”. Ann. Fac. Sci. Toulouse Math. (6) 24.4 (2015): 781-800.

  PUB | DOI
   
• [6]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980837

  Erbar, Matthias, and Huesmann, Martin. “Curvature bounds for configuration spaces”. Calc. Var. Partial Differential Equations 54.1 (2015): 397-430.

  PUB | DOI
   
• [5]
  

  2015 | Zeitschriftenaufsatz | PUB-ID: 2980836

  Erbar, Matthias, Kuwada, Kazumasa, and Sturm, Karl-Theodor. “On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces”. Invent. Math. 201.3 (2015): 993-1071.

  PUB | DOI
   
• [4]
  

  2014 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980848

  Erbar, Matthias. “Gradient flows of the entropy for jump processes”. Ann. Inst. Henri Poincaré Probab. Stat. 50.3 (2014): 920-945.

  PUB | DOI
   
• [3]
  

  2014 | Zeitschriftenaufsatz | PUB-ID: 2980850

  Erbar, Matthias, and Maas, Jan. “Gradient flow structures for discrete porous medium equations”. Discrete Contin. Dyn. Syst. 34.4 (2014): 1355-1374.

  PUB | DOI
   
• [2]
  

  2012 | Zeitschriftenaufsatz | PUB-ID: 2980852

  Erbar, Matthias, and Maas, Jan. “Ricci curvature of finite Markov chains via convexity of the entropy”. Arch. Ration. Mech. Anal. 206.3 (2012): 997-1038.

  PUB | DOI
   
• [1]
  

  2010 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2980858

  Erbar, Matthias. “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 (2010): 1-23.

  PUB | DOI