Research InterestsWahrscheinlichkeitstheorie
Project membership
Mathematics Münster

C: Models and Approximations

C1: Evolution and asymptotics
Current PublicationsGusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph Sectional Voronoi tessellations: Characterization and high-dimensional limits. Bernoulli Vol. 30 (2), 2024 online
Besau, Florian; Gusakova, Anna; Reitzner, Matthias; Schütt, Carsten; Thäle, Christoph; Werner, Elisabeth M. Spherical convex hull of random points on a wedge. Mathematische Annalen Vol. 2023, 2023 online
Gusakova, Anna; Reitzner, Matthias; Thäle, Christoph Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon. Annales Henri Lebesgue Vol. 2023 (6), 2023 online
Gusakova, Anna; Heiny, Johannes; Thäle, Christoph The volume of random simplices from elliptical distributions in high dimension. Stochastic Processes and their Applications Vol. 164, 2023 online
Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph The $β$-Delaunay tessellation IV: Mixing properties and central limit theorems. Stochastics and Dynamics Vol. 23 (3), 2023 online
Gusakova, Anna; Spodarev, Evgeny; Zaporozhets, Dmirty Intrinsic volumes of ellipsoids. Zapiski naučnyh seminarov Leningradskogo otdeleniâ ordena Lenina Matematičeskogo instituta im. V.A. Steklova Akademii nauk SSSR Vol. 515, 2022 online
Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph The $β$-Delaunay tessellation: Description of the model and geometry of typical cells. Advances in Applied Probability Vol. 54 (4), 2022 online
Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph The $β$-Delaunay tessellation II: The Gaussian limit tessellation. Electronic Journal of Probability Vol. 27, 2022 online
Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph The $β$-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions. Alea Vol. 19, 2022 online
Current ProjectsEXC 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
Phone+49 251 83-32701
FAX+49 251 83-32712
Secretary   Sekretariat Kollwitz
Frau Anita Kollwitz
Telefon +49 251 83-33770
Fax +49 251 83-32712
Zimmer 130.030
AddressFrau JProf. Dr. Anna Gusakova
Institut für Mathematische Stochastik
Fachbereich Mathematik und Informatik der Universität Münster
Orléans-Ring 10
48149 Münster
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