 |
Universität Augsburg
|
|
|
Universität Augsburg
|
|
Dr. Christian Mönch
Mainz
spricht am
Mittwoch, 7. Mai 2025
um
14 Uhr s.t.
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| I will propose a new perspective on the asymptotic regimes of fast and slow extinction of the contact process on sequences of sparse graphs: the characterisation of the phase boundary by the existence of a metastable density, which makes the study of the phase transition particularly amenable to local convergence techniques. In particular, one can derive general conditions for the coincidence of the critical threshold with the survival/extinction threshold in the local limit. I will further demonstrate that the correct time scale to separate fast extinction from slow extinction in sparse graphs is, in general, the exponential time scale, by showing that fast extinction may occur on stretched exponential time scales in fairly natural random graph models. One application of the approach, is a proof that the fast/slow threshold in sparse configuration models coincides with the survival/extinction threshold on the limiting Galton-Watson tree, which partially resolves a conjecture of Nam, Nguyen and Sly (Trans. Am. Math. Soc. 375, 2022). |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Markus Heydenreich |