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RMK Frankfurt WiSe 2018/2019


Datum: 25.01.2019

Zeit: 15:15 Uhr

Freitag, 25. Januar 2019

15:15 Uhr: Antti Knowles (Universität Genf)
Eigenvalues and eigenvectors of supercritical Erdos-Renyi graphs

Abstract: I review some recent results on Erdos-Renyi graphs G(N,p) near and above the critical scale pN = log N, where the graph undergoes a connectivity crossover. For pN >> log N, the graph G(N,p) is with high probability connected, while for pN << log N it has with high probability isolated vertices. In the supercritical regime pN >> log N, the eigenvalues stick to the bulk spectrum, a local law holds down to optimal scales, and the eigenvectors are completely delocalized. All three statements are false in the subcritical regime pN << log N. Based on joint work with F. Benaych-Georges, C. Bordenave, Y. He, and M. Marcozzi.

16:15 Uhr: Kaffee und Tee

16:45 Uhr: Aernout van Enter (Universität Groningen)
One-sided versus two-sided stochastic descriptions

Abstract: Stochastic systems can be parametrised by time (like Markov chains), in which conditioning is one-sided(the past) or by one-dimensional space (like Markov fields), where conditioning is two-sided (right and left). I will discuss some examples, in particular generalising this to g-measures versus Gibbs measures, when the two descriptions are the same and when they are different. We show the role one-dimensional entropic repulsion plays in this setting. Joint work with R. Bissacot, E. Endo and A. Le Ny

Goethe Universität Frankfurt, Campus Bockenheim, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock




Antti Knowles, Universitär Genf
Aernout C. D. van Enter, Universität Groningen


Goethe-Universität Frankfurt, Raum 711 (groß)
Institut für Mathematik, Robert-Mayer-Str. 10, 60486 Frankfurt

Campus Bockenheim, Robert-Mayer-Str. 10, Raum 711 (groß), 7. Stock

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Technische Universität Darmstadt, Johannes Gutenberg-Universität Mainz

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