| Project membership Mathematics Münster | C: Models and Approximations C1: Evolution and asymptotics |
| Current Publications | • Gusakova A, Thäle C The volume of simplices in high-dimensional Poisson-Delaunay tessellations. Annales Henri Lebesgue Vol. 4, 2021, pp 121-153 online • Gusakova A, Thäle C, Sambale H Concentration on Poisson spaces via modified $\Phi$-Sobolev inequalities. Stochastic Processes and their Applications Vol. 140, 2021, pp 216 - 235 online • Bonnet G, Gusakova A, Thäle C, Zaporozhets D Sharp inequalities for the mean distance of random points in convex body. Advances in Mathematics Vol. 386, 2021, pp 107813 online • Gusakova A, Thäle C On random convex chains, orthogonal polynomials, PF sequences and probabilistic limit theorems. Mathematika Vol. 67 (2), 2021, pp 434--446 online • Gusakova A, Kabluchko Z, Thäle C The $β$-Delaunay tessellation II: The Gaussian limit tessellation. arxiv.org/abs/2101.11316 Vol. 2021, 2021 online • Gusakova A, Kabluchko Z, Thäle C The $β$-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions. arxiv.org/abs/2104.07348 Vol. 2021, 2021 online • Gusakova A, Kabluchko Z, Thäle C The $β$-Delaunay tessellation IV: Mixing properties and central limit theorems. arxiv.org/abs/2108.09472 Vol. 2021, 2021 online • Götze F, Gusakova A, Kabluchko Z, Zaporozhets D Distribution of complex algebraic numbers on the unit circle. Journal of Mathematical Sciences Vol. 251 (1), 2020 online • Götze F, Gusakova A On the distribution of Salem numbers. Journal of Number Theory Vol. 216, 2020 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 Kollwitz Frau Anita Kollwitz 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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