Buongiorno,

Martedì 23 Maggio alle ore 14:00 in Sala di Consiglio (Dipartimento di Matematica, Università La Sapienza) avrà luogo il seguente seminario:

Speaker: Davide Gabrielli (Università dell'Aquila)

Title: HIDDEN TEMPERATURE IN THE KIPNIS-MARCHIORO-PRESUTTI MODEL

Abstract: Stationary non equilibrium states (SNS) have a rich and complex structure. The large deviations rate functionals for the empirical measure of a few one dimensional SNS of stochastic interacting systems have been computed, among which the boundary driven exclusion process and Kipnis-Marchioro-Presutti (KMP) model. The corresponding rate functionals are not local due to the presence of long range correlations. We show for the KMP model that this can be explained by introducing new variables that can be interpreted naturally as the temperatures of the oscillators that are exchanging the energies. When two oscillators exchange energy they thermalize at the same time. We deduce that the invariant measure of the boundary driven KMP model is a mixture of inhomogeneous products of exponential distributions, the law of the mixture is the invariant measure of the auxiliary temperature process. This is a joint work with Anna De Masi and Pablo Ferrari. We show moreover that a similar representation of the invariant measure holds also for the boundary driven harmonic model; in this case the hidden variables are distributed according to the order statistics of uniform random variables. This is a joint work with G. Carinci, C. Franceschini, C. Giardinà and D. Tsagkarogiannis.

Grazie dell'attenzione Saluti Alessandra