M. Birkner, L. Hartung, A. Klenke
Termine im Sommersemester 2023
Dienstag, 14 Uhr, Institut für Mathematik, Gebäude 2413, Raum 05-136
25.04.2023 |
Fu-Hsuan Ho, Université Toulouse III Algorithmic perspectives of the continuous random energy model Disordered systems have recently received much interest in the mathematical literature in terms of efficient algorithms for finding low-energy states, or sampling a typical state from the Gibbs measure. In this talk, I will discuss these algorithms in the context of the Continuous Random Energy Model (CREM), a toy model of disordered systems introduced by Derrida and Spohn in the 1980s. I will present a Gibbs Measure sampling algorithm and mention some properties of this algorithm. Then, if time permits, I will speak of a hardness result in the low-temperature regime. |
09.05.2023 |
Inhomogeneous long-range networks - an overview We revisit inhomogenous long-range percolation models in Euclidean space and give an overview of results obtained in the recent past. Particular attention is given to 'kernel-based' variants, where edge probabilities are parametrised by spatial distance of the adjacent vertices and a bivariate kernel that takes as input a pair of independent 'fitnesses' intrinsic to each vertex. The talk is partly based on several joint works with Peter Gracar (U Leeds), Markus Heydenreich (U Augsburg), Lukas Lüchtrath (WIAS Berlin) and Peter Mörters (U Köln). |
11.07.2023 |
Jan Lukas Igelbrink, JGU und Goethe-Universität Frankfurt/M. Muller's ratchet with tournament selection: Muller's ratchet is a prototype model in mathematical population genetics. In an asexual population of constant size N, individual lineages are assumed to slowly acquire slightly deleterious mutations over the generations. Due to randomness, every once and a while the individuals with the currently smallest number of mutations disappear from the population; this is a click of the ratchet. The classical variant of the model, which assumes so-called proportional selection, so far has resisted against a fully rigorous asymptotic analysis of the clicking rate. In [1] this hurdle has been overcome by considering tournament (instead of proportional) selection, where selective competition within pairs is won by the fitter individual. |
18.07.2023 |
Comparison of the random loop model to percolation and infinite Peter Mühlbacher showed that the inverse temperature of the random loop This is a joint work with Benjamin Lees and Mino Nicola Kraft. |