Prof. Dr. Hendrik Weber, Angewandte Mathematik Münster: Institut für Analysis und Numerik / Institut für Mathematische Stochastik

Member of Mathematics Münster
Investigator in Mathematics Münster
Private Homepage
Project membership
Mathematics Münster

C: Models and Approximations
B: Spaces and Operators

B3: Operator algebras & mathematical physics
C3: Interacting particle systems and phase transitions
Current Publicationsde Lima Feltes, Guilherme; Weber, Hendrik Brownian particle in the curl of 2-d stochastic heat equations. Journal of Statistical Physics Vol. 191, 2024 online
Chevyrev, I.; Gerasimovičs, A.; Weber, H. Feature Engineering with Regularity Structures. Journal of Scientific Computing Vol. 98 (13), 2024 online
Chandra, Ajay; de Lima Feltes, Guilherme; Weber, Hendrik A priori bounds for 2-d generalised Parabolic Anderson Model. , 2024 online
Chandra, Ajay; Moinat, Augustin; Weber, Hendrik A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime. Archive for Rational Mechanics and Analysis Vol. 247 (3), 2023 online
Tolomeo, Leonardo; Weber, Hendrik Phase transition for invariant measures of the focusing Schrödinger equation. , 2023 online
Grazieschi, Paolo; Matetski, Konstantin; Weber, Hendrik Martingale-driven integrals and singular SPDEs. , 2023 online
Grazieschi, Paolo; Matetski, Konstantin; Weber, Hendrik The dynamical Ising-Kac model in 3D converges to Φ43. , 2023 online
Bruno, Stefano; Gess, Benjamin; Weber, Hendrik Optimal regularity in time and space for stochastic porous medium equations. Annals of Probability Vol. 50 (6), 2022 online
Gunaratnam, Trishen; Oh, Tadahiro; Tzvetkov, Nikolay; Weber, Hendrik Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions. Probability and Mathematical Physics Vol. 3 (2), 2022 online
Current ProjectsGlobal Estimates for non-linear stochastic PDEs

Semi-linear stochastic partial differential equations: global solutions’ behaviours
Partial differential equations are fundamental to describing processes in which one variable is dependent on two or more others – most situations in real life. Stochastic partial differential equations (SPDEs) describe physical systems subject to random effects. In the description of scaling limits of interacting particle systems and in quantum field theories analysis, the randomness is due to fluctuations related to noise terms on all length scales. The presence of a non-linear term can lead to divergencies. Funded by the European Research Council, the GE4SPDE project will describe the global behaviour of solutions of some of the most prominent examples of semi-linear SPDEs, building on the systematic treatment of the renormalisation procedure used to deal with these divergencies.

EXC 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-Mailhendrik dot weber at uni-muenster dot de
Phone+49 251 83-35148
FAX+49 251 83-32729
Secretary   Sekretariat Lückert
Frau Dr. Claudia Lückert
Telefon +49 251 83-35154
Fax +49 251 83-32729
Zimmer 120.025
AddressProf. Dr. Hendrik Weber
Angewandte Mathematik Münster: Institut für Analysis und Numerik
Fachbereich Mathematik und Informatik der Universität Münster
Orléans-Ring 10
48149 Münster
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