# Prof. Dr. Martin Huesmann, Institut für Mathematische Stochastik

Member of Mathematics MünsterInvestigator in Mathematics Münster

Investigator in Mathematics Münster

Private Homepage | https://www.uni-muenster.de/Stochastik/Arbeitsgruppen/Huesmann/ |

Research Interests | optimal transport stochastic mass transfer, martingale optimal transport, causal transport matching and allocation problems robust finance random measures, point processes |

Project membershipMathematics Münster | C: Models and ApproximationsC1: Evolution and asymptotics |

Current Publications | • Backhoff-Veraguas J, Beiglböck M, Huesmann M, Källblad S Martingale Benamou-Brenier: a probabilistic perspective. Ann. Probab. Vol. 48 (5), 2020 online• Beiglböck M, Cox AMG, Huesmann M The geometry of multi-marginal Skorokhod Embedding. Probability Theory and Related Fields Vol. 176, 2020 online• Huesmann M, Trevisan D A Benamou-Brenier formulation of martingale optimal transport. Bernoulli Vol. 25 (4A), 2019, pp 2729-2757 online• Huesmann M, Stebegg F Monotonicity preserving transformations of MOT and SEP. Stochastic Processes and their Applications Vol. 128 (4), 2018, pp 1114-1134 online |

Current Projects | • SPP 2265: Random Geometric Systems - Subproject: Optimal transport for stationary point processes Optimal transport by now has found manifold applications in various areas of mathematics, in particular it has turned into a powerful tool in the analysis of stochastic processes, particle dynamics, and the associated evolution equations, mostly however in a finite-dimensional setting. The goal of this project is to develop a counterpart to this theory in the framework of stationary point processes or more general random (infinite) measures and to employ these novel tools e.g. in the analysis of infinite particle dynamics or to attack questions for particular point process models of interest. online• SPP 2265: Random Geometric Systems - Subproject: Optimal matching and balancing transport The optimal matching problem is one of the classical problems in probability. By now, there is a good understanding of the macroscopic behaviour with some very detailed results, several challenging predictions, and open problems. The goal of this project is to develop a refined analysis of solutions to the optimal matching problem from a macroscopic scale down to a microscopic scale. Based on a recent quantitative linearization result of the Monge-Ampère equation developed in collaboration with Michael Goldman, we will investigate two main directions. On the one hand, we aim at rigorously connecting the solutions to the optimal matching problem to a Gaussian field which scales as the Gaussian free field. On the other hand, we seek to close the gap and show that rescaled solutions to the optimal matching problem converge in the thermo-dynamic limit to invariant allocations to point processes, or more generally to balancing transports between random measures. In the long run, combining these limit results with the Gaussian like behaviour of solutions to the matching problem, we seek to analyse the random tessellations induced by the limiting invariant allocations. online• EXC 2044 - C1: Evolution and asymptotics In this unit, we will use generalisations of optimal transport metrics to develop gradient flow descriptions of (cross)-diffusion-reaction systems, rigorously analyse their pattern forming properties, and develop corresponding efficient numerical schemes. Related transport-type- and hyperbolic systems will be compared with respect to their pattern-forming behaviour, especially when mass is conserved. Bifurcations and the effects of noise perturbations will be explored.Moreover, we aim to understand defect structures, their stability and their interactions. Examples are the evolution of fractures in brittle materials and of vortices in fluids. Our analysis will explore the underlying geometry of defect dynamics such as gradient descents or Hamiltonian structures. Also, we will further develop continuum mechanics and asymptotic descriptions for multiple bodies which deform, divide, move, and dynamically attach to each other in order to better describe the bio-mechanics of growing and dividing soft tissues. Finally, we are interested in the asymptotic analysis of various random structures as the size or the dimension of the structure goes to infinity. More specifically, we shall consider random polytopes and random trees.For random polytopes we would like to compute the expected number of faces in all dimensions, the expected (intrinsic) volume, and absorption probabilities, as well as higher moments and limit distributions for these quantities. online |

E-Mail | martin dot huesmann at uni-muenster dot de |

Phone | +49 251 83-35086 |

FAX | +49 251 83-32712 |

Room | 130.017 |

Secretary | Sekretariat Kollwitz Frau Anita Kollwitz Telefon +49 251 83-33770 Fax +49 251 83-32712 Zimmer 130.030 |

Address | Prof. Dr. Martin Huesmann Institut für Mathematische Stochastik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |

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