Multiple shocks in bricklayers' model

Abstract

In bricklayers' model, which is a generalization of the misanthrope processes, we show that a nontrivial class of product distributions is closed under the time-evolution of the process. This class also includes measures fitting to shock data of the limiting PDE. In particular, we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting, in an attractive way, via their jump rates. Our results are related to those of Belitsky and Schuetz on the simple exclusion process, although we do not use quantum formalism as they do. The structures we find are described from a fixed position. Similar ones were found in a paper by Balazs, as seen from the random position of the second class particle.

More detailed explanations and a few additional arguments are added, the paper is hopefully more clear now. LaTeX 2e, 22 pages, submitted to Journal of Stat. Phys

References in corpus (5)

• Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension
• The Asymmetric Simple Exclusion Process with Multiple Shocks
• Growth fluctuations in a class of deposition models
• Microscopic shape of shocks in a domain growth model
• Between equilibrium fluctuations and Eulerian scaling: Perturbation of equilibrium for a class of deposition models

Cited by in corpus (7)

• Random walk of second class particles in product shock measures
• Existence of the zero range process and a deposition model with superlinear growth rates
• A reverse duality for the ASEP with open boundaries
• Ergodicity breaking in one-dimensional reaction-diffusion systems
• Fluctuation bounds in the exponential bricklayers process
• Q-zero range has random walking shocks
• Multi-species reaction-diffusion models admitting shock solutions