Publikationen

Preprint

• Gap metrics for stationary point processes and quantitative convexity of the free energy
  joint work with Bastian Müller
  [arXiv]
• Non-local Wasserstein Geometry, Gradient Flows, and Functional Inequalities for Stationary Point Processes
  joint work with Hanna Stange
  [arXiv]
• Asymptotics for Random Quadratic Transportation Costs
  joint work with Michael Goldman and Dario Trevisan
  [arXiv]
• (Non)-hyperuniformity of perturbed lattices
  joint work with David Dereudre, Daniela Flimmel, and Thomas Leblé
  [arXiv]
• The link between hyperuniformity, Coulomb energy, and Wasserstein distance to Lebesgue for two-dimensional point processes
  joint work with Thomas Leblé
  [arXiv]
• Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem
  joint work with Michael Goldman and Felix Otto
  [arXiv]
• Measure valued martingales and optimality of Bass-type solutions to the Skorokhod embedding problem
  joint work with Mathias Beiglboeck, Alex Cox and Sigrid Kaellblad
  [arXiv]

Publications

• A Benamou-Brenier formula for transport distances between stationary random measures
  joint work with Bastian Müller
  Stochastic Processes Appl. 185, Article ID 104633, 21 p. (2025).
  [arXiv]
• There is no stationary p-cyclically monotone Poisson matching in 2d
  joint work with Francesco Mattesini and Felix Otto
  Electron. J. Probab. 29, Paper No. 106, 20 p. (2024).
  [arXiv]
• Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy
  joint work with Matthias Erbar, Jonas Jalowy, and Bastian Müller
  J. Funct. Anal. 289, No. 4, Article ID 110974, 67 p. (2025).
  [arXiv]
• Transportation of random measures not charging small sets
  joint work with Bastian Müller
  ALEA, 21, 1903–1913 (2024)
  [arXiv]
• There is no stationary cyclically monotone Poisson matching in 2d
  joint work with Francesco Mattesini and Felix Otto
  Probab. Theory Relat. Fields, online first
  [arXiv]
• Shadows and Barriers
  joint work with Martin Brückerhoff
  Ann. Appl. Probab., to appear
  [arXiv]
• Switching Identities by Probabilistic Means
  joint work with Julio Backhoff, Alex Cox, and Anne Grass
  to appear in Séminaire de Probabilités
  [arXiv]
• Shadow martingales - a stochastic mass transport approach to the peacock problem
  joint work with Martin Brückerhoff and Nicolas Juillet
  Electronic Journal of Probability, Vol 27 (2022), paper no. 127, 62p.
  [arXiv]
• Wasserstein Asymptotics for the Empirical Measure of Fractional Brownian Motion on a Flat Torus
  joint work with Francesco Mattesini and Dario Trevisan
  Stochastic Processes and their Application, Vol 155, January 2023, Pages 1-26
  [arXiv]
• A fluctuation result for the displacement in the optimal matching problem
  joint work with Michael Goldman
  Ann. Probab. 50(4): 1446-1477 (July 2022).
  [arXiv]
• Quantitative linearization results for the Monge-Ampère equation
  joint work with Michael Goldman and Felix Otto
  Comm. Pure Appl. Math  74 (12), 2483-2560, 2021
  [arXiv]
• Model independent pricing with insider information: a Skorokhod embedding approach
  joint work with Beatrice Acciaio and Alex Cox
  Adv. in Appl. Probab. 53(1), 30-56, 2021
  [arxiv]
• The one-dimensional log-gas free energy has a unique minimiser
  joint work with Matthias Erbar and Thomas Leble
  Comm. Pure Appl. Math., 74: 615-675.
  [arXiv]
• Martingale Benamou-Brenier: a probabilistic perspective
  joint work with Julio Backhoff, Mathias Beiglboeck, and Sigrid Kaellblad
  Ann. Probab. 48(5): 2258-2289, 2020
  [arXiv]
• The geometry of multi-marginal Skorokhod embedding
  joint work with Mathias Beiglboeck and Alex Cox
  Probab. Theory Relat. Fields 176: 1045–1096, 2020
  [arxiv]
• A Benamou-Brenier formulation of martingale optimal transport
  joint work with Dario Trevisan
  Bernoulli 25(4A):2729-2757, 2019
  [arXiv]
• Monotonicity preserving transformations of MOT and SEP
  joint work with Florian Stebegg
  Stoch. Proc. Appl., 128(4):1114-1134, 2018
  [arXiv]
• Pathwise superreplication via Vovk's outer measure
  joint work with Mathias Beiglboeck, Alex Cox, Nicolas Perkowski, and David Proemel.
  Finance Stoch., 21(4):1141-1166, 2017
  [arXiv]
• Optimal transport and Skorokhod embedding
  joint work with Mathias Beiglboeck and Alex Cox
  Invent. Math., 208(2):327-400, 2017
  [arXiv]
• Transport cost estimates for random measures in dimension one
  Electron. Commun. Probab. 21, paper no. 46, 2016
  [arXiv]
• Root to Kellerer
  joint work with Mathias Beiglboeck and Florian Stebegg
  Seminaire de Probabilites XLVIII, 1-12, 2016
  [arXiv]
• Curvature bounds for configuration spaces
  joint work with Matthias Erbar
  Calc. Var. Partial Differ. Equ., 54(1):397-430, 2014
  [arXiv]
• Existence and uniqueness of optimal transport maps
  joint work with Fabio Cavalletti
  Ann. Inst. Henri Poincare, Anal. Non Lineaire, 32(6):1367-1377, 2015
  [arXiv]
• Self-intersection of optimal geodesics
  joint work with Fabio Cavalletti
  Bull. Lond. Math. Soc., 46(3):653-656,2014
  [arXiv]
• Optimal transport between random measures
  Annales de l'Institut Henri Poincare (B) 52 (2016), no. 1, 196--232.
  [arXiv]
• Optimal transport from Lebesgue to Poisson
  joint work with Karl-Theodor Sturm
  Annals of Probability 41 (2013), no. 4, 2426--2478.
  [arXiv]
• From random walks to rough paths
  joint work with Emmanuel Breuillard and Peter Friz
  Proc. Amer. Math. Soc. 137 (2009), no. 10, 3487--3496
  [arXiv]

Unpublished Notes

• A large scale regularity theory for the Monge-Ampere equation with rough data and application to the matching problem
  joint work with Michael Goldmann and Felix Otto
  [arXiv]