Teaching
WS 2024/25 Optimal Transport Masterseminar: Stochastic Analysis SS 2024 Masterseminar: Mathematical Statistical Mechanics WS 2023/24 Stochastic Analysis MSc Seminar: Optimal Transport SS 2023 Optimal Transport WS 2022/23 Stochastic Analysis MSc Seminar: Ising model WS 2021/22 Probability Theory II BSc Seminar: Large Deviations SS 2021 Probability Theory MSc Seminar: Stochastic Processes WS 2020/2021 Stochastik MSc Seminar: Gaussian processes SS 2020 Stochastic Mass Transport BSc/MSc Seminar: Stochastische Homogenisierung WS 2019/2020 Stochastic Analysis BSc Seminar: Empirical measures and transport metrics Publications
Preprint
- 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] - A Benamou-Brenier formula for transport distances between stationary random measures
joint work with Bastian Müller
[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] - There is no stationary p-cyclically monotone Poisson matching in 2d
joint work with Francesco Mattesini and Felix Otto
[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
[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]
- Asymptotics for Random Quadratic Transportation Costs