15/06/2022, 17:00 — 18:00 — Online
Christophe Bahadoran, Université Blaise Pascal, Clermont-Ferrand
Invariant measures for multilane exclusion process
Invariant measures for the one-dimensional asymmetric exclusion process (ASEP) are fairly well (though not entirely) understood. Under broad assumptions they consist of homogeneous Bernoulli measures and blocking measures. In several dimensions, the characterization of invariant measures (outside translation invariant ones) is still open. Bramson and Liggett (AOP 2005) laid important foundations and formulated conjectures. In particular they introduced a family of d-dimensional blocking-type measures as reasonable candidates for characterization. Here we study an intermediate model, the multilane ASEP or ladder process,that is a 2d ASEP where one direction is finite and the dynamics is translation invariant in the infinite direction. We obtain characterization results for invariant measures involving product measures homogeneous in the infinite direction and 2d blocking measures with the same flavour as Bramson and Liggett's.
Joint work with G. Amir, O. Busani and E. Saada.
