Dear All, next Tuesday Nicolas Forien (Sapienza Università di Roma) will give a seminar talk on particle systems and interacting random walks. Please find the title and the abstract below. Best regards, Lorenzo Taggi

Tuesday 31st of May, 16.15, Dipartimento di Matematica Università Sapienza, Aula Consiglio

*Title:* On the phase transition of activated random walks

*Abstract:* The Activated Random Walk model consists of particles which perform independent random walks on a graph and fall asleep with a certain rate. Sleeping particles stop moving and are awaken when another particle arrives on the same site. The model on Z^d presents a phase transition: depending on the density of particles (initially all active) and on the sleep rate, either almost surely each particle eventually falls asleep forever (fixating phase), or almost surely no particle falls asleep forever (active phase). In this talk, I will present a joint work with Alexandre Gaudillière (arxiv.org/abs/2203.02476) showing the existence of an active phase on Z^2: for every positive initial density of particles, for a sufficiently low sleep rate, almost surely no particle falls asleep forever.