Work

Second order Boltzmann-Gibbs principle for polynomial functions and applications

Year: 2015

Type: preprint

Abstract: In this paper we give a new proof of the second order Boltzmann-Gibbs principle. 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 supper-diffusive systems, 2) an Ornstein-Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1507.06076

Authors: Gonçalves, Patricia, Jara, Milton, Simon, Marielle

Institutions: University of Lisbon, Instituto Nacional de Matemática Pura e Aplicada, Instituto Superior Técnico, Centre Inria de l'Université de Lille

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação para a Ciência e a Tecnologia

Awards: Energy Diffusion in Noisy Hamiltonian Systems, G3257718068, Centre Européen pour les Mathématiques, la Physique et leurs Interactions, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, G5903895508, G8238292487

OpenAlex ID: W2951963116

Cites: 6

Cited by: 3

Related to: 20