Seminar on Analysis and Probability, organized by the Faculty of Mathematics HSE. Speaker: Cristian Giardina

Abstract:

We introduce and discuss the "harmonic model", an integrable Markov process describing heat conduction in interacting particle systems. The model is closely related to the celebrated Kipnis-Marchioro-Presutti (KMP) process. In particular, the two models share an $\mathfrak{sl}_2$ symmetry, which underlies their dualities, although they differ in their energy redistribution rule. Furthermore, the harmonic model is integrable in the sense of Yang-Baxter. Exploiting this structure, we compute the non-equilibrium steady state in closed

form. We show that it can be expressed as a mixture of product Gibbs distributions, with local temperatures given by the ordered Dirichlet distribution. As a consequence, we prove that the empirical energy profile satisfies a large deviation principle, with a rate function in agreement with the prediction of Macroscopic Fluctuation Theory.

Seminar's page https://math.hse.ru/en/Sem_Analys-Probab_FM/