Diffusivity of lattice gases

Abstract

We consider one component lattice gases with a local dynamics and a stationary product Bernoulli measure. We give upper and lower bounds on the diffusivity at an equilibrium point depending on the dimension and the local behavior of the macroscopic flux function. We show that if the model is expected to be diffusive, it is indeed diffusive, and, if it is expected to be superdiffusive, it is indeed superdiffusive.

39 pages, 1 figure

References in corpus (5)

• Renormalization fixed point of the KPZ universality class
• $t^{1/3}$ Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on $\mathbb{Z}$
• Universality of KPZ equation
• Hydrodynamic limit of particle systems with long jumps
• Macroscopic energy diffusion for a chain of anharmonic oscillators

Cited by in corpus (4)

• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
• Logarithmic superdiffusion in two dimensional driven lattice gases
• Diffusion and superdiffusion in lattice models of colliding particles with stored momentum