2004/02/02 by Benedek Valkó, Benedek Valko, Valko, Benedek
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.AP #math.PR
paper · pdf · doi:10.48550/arxiv.math/0402017
21 pages
arxiv created 2004/02/02 · openalex publication_date 2004/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider one-dimensional, locally finite interacting particle systems with two conservation laws. The models have a family of stationary measures with product structure and we assume the existence of a uniform bound on the inverse of the spectral gap which is quadratic in the size of the system. Under Eulerian scaling the hydrodynamic limit for the macroscopic density profiles leads to a two-component system of conservation laws. The resulting pde is hyperbolic inside the physical domain of the macroscopic densities, with possible loss of hyperbolicity at the boundary. We investigate the propagation of small perturbations around a hyperbolic equilibrium point. We prove that the perturbations essentially evolve according to two decoupled Burgers equations. The scaling is not Eulerian: if the lattice constant is n-1, the perturbations are of order n-β then time is speeded up by n1+\b. Our derivation holds for 0