The random walk on dynamic environments, such as the simple exclusion process (SEP) on a d-dimensional lattice, has attracted considerable attention in the last decade. In this model, a random walker moves at each unit of time to a neighbouring vertex, with a drift that depends on whether its current location is occupied or not by a SEP particle.

We will focus on the case d=1, when occupied sites have a drift to the right, and empty sites a drift to the left. The parameter of interest will be the density of particles: when it is large (resp. small), the random walk has a positive (resp. negative) speed.

Since the SEP is conservative and mixes slowly, a natural question is whether there are strong trapping effects, as in the more classical setting of static environments. Could it be for instance that for a non-empty interval of intermediate densities, the random walk has zero speed? We give a negative answer, showing that the speed is strictly increasing with the density.

The proof uses a comparison with a finite-range model (via renormalisation), and an original coupling to circumvent the bad mixing properties of the SEP.

This is joint work with Daniel Kious and Pierre-François Rodriguez.

Date: 20 May 2024, 14:00 (Monday, 5th week, Trinity 2024)

Venue: Venue to be announced

Speaker: Guillaume Conchon-Kerjan (King College London)

Organising department: Department of Statistics

Organisers: Matthias Winkel (Department of Statistics, University of Oxford), Julien Berestycki (University of Oxford), Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)

Part of: Probability seminar

Booking required?: Not required

Audience: Members of the University only

Editor: Julien Berestycki