Higher-order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems

#### J.P. Chen, F. Sau

2021, v.27, Issue 3, 339-380

ABSTRACT

Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the $d$-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider$d$-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields.

Keywords: Interacting particle systems; Higher-order fields; Hydrodynamic limit; Equilibrium fluctuations; Duality