The Enskog Process |
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Authors: | S Albeverio B Rüdiger P Sundar |
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Institution: | 1.Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico,Universidade de Lisboa,Lisbon,Portugal;2.Instituto de Matemática Pura e Aplicada,Rio de Janeiro,Brazil;3.équipe MEPHYSTO, Inria Lille – Nord Europe,Villeneuve d’Ascq,France |
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Abstract: | In this paper we give a new proof of the second order Boltzmann–Gibbs principle introduced in Gonçalves and Jara (Arch Ration Mech Anal 212(2):597–644, 2014). The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards (1) a trivial process in case of super-diffusive systems, (2) an Ornstein–Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, as defined in Gubinelli and Jara (SPDEs Anal Comput (1):325–350, 2013) and Gubinelli and Perkowski (Arxiv:1508.07764, 2015), in case of weakly asymmetric diffusive systems. Examples and applications are presented for weakly and partial asymmetric exclusion processes, weakly asymmetric speed change exclusion processes and hamiltonian systems with exponential interactions. |
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