### The totally asymmetric simple exclusion process on Galton-Watson trees.

Probability Seminar

24th March 2023, 3:30 pm – 4:30 pm

Fry Building, 2.04

We define a totally asymmetric simple exclusion process on trees, where the particles enter the tree from a reservoir attached to the root. Particles can only jump following edges on the tree and only if they are jumping away from the root, to a non-occupied vertex.

We are interested in two different aspects of this particle system. First we want to investigate the current of particles across a given generation at a specific time, when we start from an initially empty initial condition. Second, we would like to obtain some information about the limiting equilibrium measures. Both answers depend heavily on our choice of jump rates for the particles and different regimes of behaviour will be presented during the talk. Our results rely on a crucial estimate of the time it takes for the trajectories of the first N particles to decouple in the tree.

Due to the time constraint there will be a live audience participation to decide the order of the presentation in a democratic way 🙂

This is joint work with N. Gantert (TUM) and D. Schmid (Princeton and UBonn)

## Comments are closed.