Lorenzo Bertini -- Current fluctuations in stochastic lattice gases: Donsker-Varadhan meets Freidlin-Wentzell

schedule le vendredi 17 décembre 2021 de 11h00 à 12h00

Organisé par : Q. Berger, N. Enriquez, T. Lévy, S. Lin

Intervenant : Lorenzo Bertini (La Sapienza, Roma)
Lieu : Jussieu, salle Paul Lévy, 16-26 - 209

Sujet : Current fluctuations in stochastic lattice gases: Donsker-Varadhan meets Freidlin-Wentzell

Résumé :

We discuss the large deviations asymptotic of the time-averaged empirical current in stochastic lattice gases in the limit in which both the number of particles and the time window diverge. For some models it has been shown that dynamical phase transitions occur: the optimal density profile to realize such deviations is given by travelling waves rather than by homogeneous profiles. We shall prove a variational representation, proposed by Varadhan, for the corresponding rate function that is obtained by projecting the large deviations at the level of the empirical process.