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RMK Darmstadt


Siva Athreya:Graphon dynamics from population genetics; Maria Deijfen:Competing frogs on Z^d

Datum: 22.01.2021

Zeit: 15:15–17:45 Uhr

Zoom access to the talks:
Meeting-ID: 827 7869 9254
Code: 559655
15:15-16:15 Siva Athreya (Bengaluru) Title: Graphon dynamics from population genetics 
In this talk we shall discuss a natural class of dynamics in dense networks arising from resampling in multi-type populations. We
consider sequence of finite graphs whose dynamics are governed by the empirical type distribution of the whole population at that time
and in the large-population-size limit this dynamics converges to a random process in the space of graphons. This is joint work with Frank
den Hollander and Adrian Rollin.
16:15-16:45 virtual coffee break 
Access to the virtual coffee breaks:
We have two virtual rooms (each can host up to 25 people):
16:45-17:45 Mia Deijfen (Stockholm) Title: Competing frogs on Z^d
The so called frog model on Z^d is driven by moving particles on the sites of the Z^d -lattice. Each site is independently assigned a random
number of particles. At time 0, the particles at the origin are activated, while all other particles are sleeping. When a particle is
activated, it starts moving according to a simple random walk and, when a site is visited by an active particle, any sleeping particles at the
site are activated and start moving. I will describe a two-type version of the model, where an active particle can be of either of two types.
For this model, a natural question is whether the types can coexist in the sense that they both activate infinitely many particles. I will
describe existing results and open problems related to this.


Maria Deijfen, Stockholm University
Siva Athreya, Indian Statistical Institute, Bengaluru


Via Zoom




Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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