Mixing times of exclusion processes on regular graphs

Place k black particles and n-k white particles on the vertices of an n vertex graph, with one per vertex. Suppose each edge rings at rate 1 independently, and when an edge rings particles at the end-points switch positions. Oliveira conjectured that this “k-particle exclusion process” has mixing time of order at most that of k independent particles. Together with Jonathan Hermon we prove a bound for regular graphs which is in general within a log log n factor from this conjecture when k>n^c and which, in certain cases, verifies the conjecture. As a result we obtain new mixing time bounds for the exclusion process on expanders and the hypercube.

• Speaker: Richard Pymar (Birkbeck)
• Tuesday 19 February 2019, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.