Private Homepagehttps://www.uni-muenster.de/Stochastik/Arbeitsgruppen/Huesmann/
Research Interestsoptimal transport
stochastic analysis
random measures, point processes
stochastic mass transfer, martingale optimal transport, causal transport
matching and allocation problems
robust finance
Selected PublicationsBeiglböck M, Cox AMG, Huesmann M Optimal transport and Skorokhod embedding. Inventiones Mathematicae Vol. 208 (2), 2017, pp 327-400 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, Sturm K Optimal transport from Lebesgue to Poisson. Ann. Probab. Vol. 41 (4), 2013, pp 2426-2478 online
Backhoff-Veraguas J, Beiglböck M, Huesmann M, Källblad S Martingale Benamou-Brenier: a probabilistic perspective. Ann. Probab. Vol. 48 (5), 2020 online
Topics in
Mathematics Münster


T5: Curvature, shape, and global analysis
T8: Random discrete structures and their limits
Current PublicationsAcciaio B, Cox AM, Huesmann M Model-independent pricing with insider information: a Skorokhod embedding approach. Adv. in Appl. Probab. Vol. 53 (1), 2021 online
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 ProjectsGRK 3027: Rigorous Analysis of Complex Random Systems

The Research Training Group is dedicated to educating mathematicians in the field of complex random systems. It provides a strong platform for the development of both industrial and academic careers for its graduate students. The central theme is a mathematically rigorous understanding of how probabilistic systems, modelled on a microscopic level, behave effectively at a macroscopic scale. A quintessential example for this RTG lies in statistical mechanics, where systems comprising an astronomical number of particles, upwards of 10^{23}, can be accurately described by a handful of observables including temperature and entropy. Other examples come from stochastic homogenisation in material sciences, from the behaviour of training algorithms in machine learning, and from geometric discrete structures build from point processes or random graphs. The challenge to understand these phenomena with mathematical rigour has been and continues to be a source of exciting research in probability theory. Within this RTG we strive for macroscopic representations of such complex random systems. It is the main research focus of this RTG to advance (tools for) both qualitative and quantitative analyses of random complex systems using macroscopic/effective variables and to unveil deeper insights into the nature of these intricate mathematical constructs. We will employ a blend of tools from discrete to continuous probability including point processes, large deviations, stochastic analysis and stochastic approximation arguments. Importantly, the techniques that we will use and the underlying mathematical ideas are universal across projects coming from completely different origin. This particular facet stands as a cornerstone within the RTG, holding significant importance for the participating students. For our students to be able to exploit the synergies between the different projects, they will pass through a structured and rich qualification programme with several specialised courses, regular colloquia and seminars, working groups, and yearly retreats. Moreover, the PhD students will benefit from the lively mathematical community in Münster with a mentoring programme and several interaction and networking activities with other mathematicians and the local industry.

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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-Mailmartin dot huesmann at uni-muenster dot de
Phone+49 251 83-35086
FAX+49 251 83-32712
Room130.017
Secretary   Sekretariat Stochastik
Frau Claudia Giesbert
Telefon +49 251 83-33792
Fax +49 251 83-32712
Zimmer 120.002
AddressProf. Dr. Martin Huesmann
Institut für Mathematische Stochastik
Fachbereich Mathematik und Informatik der Universität Münster
Orléans-Ring 10
48149 Münster
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