Mathematik und Informatik
© FB 10

Prof. Dr. Matthias Löwe, Institut für Mathematische Stochastik

Investigator in Mathematics Münster

Sprechstunde: nach Vereinbarung
Private Homepage
Research InterestsTheory of Random Walks
Spin Glasses and Statistical Mechanics
Algorithms and their Speed of Convergence
Neural Networks
Non-Parametric Statistics and Large Deviations
Particle Models in Mathematical Economics and Finance
Project membership
Mathematics Münster

C: Models and Approximations
B: Spaces and Operators

C3: Interacting particle systems and phase transitions
B3: Operator algebras & mathematical physics
Current PublicationsLöwe, Matthias; Terveer, Sara A Central Limit Theorem for incomplete U-statistics over triangular arrays. Brazilian Journal of Probability and Statistics Vol. 35 (3), 2021 online
Current ProjectsEXC 2044 - B3: Operator algebras & mathematical physics The development of operator algebras was largely motivated by physics since they provide the right mathematical framework for quantum mechanics. Since then, operator algebras have turned into a subject of their own. We will pursue the many fascinating connections to (functional) analysis, algebra, topology, group theory and logic, and eventually connect back to mathematical physics via random matrices and non-commutative geometry. online
EXC 2044 - C3: Interacting particle systems and phase transitions The question of whether a system undergoes phase transitions and what the critical parameters are is intrinsically related to the structure and geometry of the underlying space. We will study such phase transitions for variational models, for processes in random environments, for interacting particle systems, and for complex networks. Of special interest are the combined effects of fine-scalerandomly distributed heterogeneities and small gradient perturbations.

We aim to connect different existing variational formulations for transportation networks, image segmentation, and fracture mechanics and explore the resulting implications on modelling, analysis, and numerical simulation of such processes. We will study various aspects of complex networks, i.e. sequences of random graphs (Gn)n∈N, asking for limit theorems as n tends to infinity. A main task will be to broaden the class of networks that can be investigated, in particular, models which include geometry and evolve in time. We will study Ising models on random networks or with random interactions, i.e. spin glasses. Fluctuations of order parameters and free energies will be analysed, especially at the critical values where the system undergoes a phase transition. We will also investigate whether a new class of interacting quantum fields connected with random matrices and non-commutative geometry satisfies the Osterwalder-Schrader axioms. Further, we will study condensation phenomena, where complex network models combine the preferential attachment paradigm with the concept of fitness. In the condensation regime, a certain fraction of the total mass dynamically accumulates at one point, the condensate. The aim is a qualitative and quantitative analysis of the condensation. We willalso explore connections to structured population models. Further, we will study interacting particle systems on graphs that describe social interaction or information exchange. Examples are the averaging process or the Deffuant model.

We will also analyse asymmetric exclusion processes (ASEP) on arbitrary network structures. An interesting aspect will be how these processes are influenced by different distribution mechanisms of the particles at networks nodes. If the graph is given by a lattice, we aim to derive hydrodynamic limits for the ASEP with jumps of different ranges for multiple species, and for stochastic interactingmany-particle models of reinforced random walks. Formally, local cross-diffusion syste ms are obtained as limits of the classical multi-species ASEP and of the many-particle random walk. We will compare the newly resulting limiting equations and are interested in fluctuations, pattern formation, and the long-time behaviour of these models on the microscopic and the macroscopic scale. Further, we will analyse properties of the continuous directed polymer in a random environment. online
E-Mailmaloewe at uni-muenster dot de
Phone+49 251 83-33774
FAX+49 251 83-32712
Secretary   Sekretariat Kollwitz
Frau Anita Kollwitz
Telefon +49 251 83-33770
Fax +49 251 83-32712
Zimmer 130.030
AddressProf. Dr. Matthias Löwe
Institut für Mathematische Stochastik
Fachbereich Mathematik und Informatik der Universität Münster
Orléans-Ring 10
48149 Münster
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