Publications

Preprint

• 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
  [arXiv]
• Transportation of random measures not charging small sets
  joint work with Bastian Müller
  [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

• 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]