| Research Interests | Wahrscheinlichkeitstheorie |
| Topics in Mathematics Münster | T8: Random discrete structures and their limits |
| Current Publications | • Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph Sectional Voronoi tessellations: Characterization and high-dimensional limits. Bernoulli Vol. 30 (2), 2024 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 • 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: 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. Latin American Journal of Probability and Mathematical Statistics Vol. 19, 2022 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 |
| Current Projects | • 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 | gusakova@uni-muenster.de |
| Phone | +49 251 83-32701 |
| FAX | +49 251 83-32712 |
| Room | 130.027 |
| Secretary | Sekretariat Stochastik Frau Yvonne (Stochastik) Stein Telefon +49 251 83-33770 Fax +49 251 83-32712 Zimmer 130.030 |
| Address | Frau JProf. Dr. Anna Gusakova Institut für Mathematische Stochastik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |
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