Dear Colleagues,

We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi (abstract below):

Too many frogs cannot fall sleep by Alexandre Gaudillière (CNRS)

The seminars will take place on TUE, 10.10.2023 at 11:00 CET in Aula Tricerri, Dipartimento di Matematica e Informatica “Ulisse Dini", University of Florence and streamed online (see seminar website for the URL).

The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass https://www.google.com/url?q=https://www.google.com/url?q%3Dhttps://sites.google.com/unipi.it/spass%26source%3Dgmail-imap%26ust%3D1665669490000000%26usg%3DAOvVaw07o0tKOUGmZjDDF2Ta7pQY&source=gmail-imap&ust=1694611307000000&usg=AOvVaw3yf_2XYyZ0yUTh9Kbq6j_p

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Too many frogs cannot fall sleep

Abstract: We prove the existence of an active phase for activated random walks on the lattice in all dimensions. This interacting particle system is made of two kinds of random walkers, or frogs: active and sleeping frogs. Active frogs perform simple random walks, wake up all sleeping frogs on their trajectory and fall asleep at constant rate $\lambda$. Sleeping frogs stay where they are up to activation, when waken up by an active frog.

At a large enough density, which is increasing in $\lambda$ but always less than one, such frogs on the torus form a metastable system. We prove that $n$ active frogs in a cramped torus will typically need an exponentially long time to collectively fall asleep ---exponentially long in $n$.

This completes the proof of existence of a non-trivial phase transition for this model designed for the study of self-organized criticality. This is a joint work with Amine Asselah and Nicolas Forien.

---------------------------------------------------------------------- Gianmarco Bet (he/him) Senior researcher

https://gianmarco.bet Phone: (+39) 055 2751491

Department of Mathematics and Computer Science "U. Dini" University of Florence Viale Morgagni, 65 50134 Firenze, Italy Office 64 ----------------------------------------------------------------------