Exact connections between current fluctuations and the second class particle in a class of deposition models

Abstract

We consider a large class of nearest neighbor attractive stochastic interacting systems that includes the asymmetric simple exclusion, zero range, bricklayers' and the symmetric K-exclusion processes. We provide exact formulas that connect particle flux (or surface growth) fluctuations to the two-point function of the process and to the motion of the second class particle. Such connections have only been available for simple exclusion where they were of great use in particle current fluctuation investigations.

Second version, results a bit more clear; 23 pages

References in corpus (4)

• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• $t^{1/3}$ Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on $\mathbb{Z}$
• Existence of the zero range process and a deposition model with superlinear growth rates
• Growth fluctuations in a class of deposition models

Cited by in corpus (7)

• Random walk of second class particles in product shock measures
• Microscopic concavity and fluctuation bounds in a class of deposition processes
• Order of current variance and diffusivity in the rate one totally asymmetric zero range process
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• Fluctuation bounds in the exponential bricklayers process
• Universal scaling for second class particles in a one-dimensional misanthrope process
• Occupation times of long-range exclusion and connections to KPZ class exponents