Stationary coalescing walks on the lattice II: Entropy
Abstract
This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Z^d. We assume that once walks meet, they coalesce. We consider various entropic properties of these systems. We show that in systems with completely positive entropy, bi-infinite trajectories must carry entropy. In the case of directed walks in dimension 2 we show that positive entropy guarantees that all trajectories cannot be bi-infinite. To show that our theorems are proper, we construct a stationary discrete-time symmetric exclusion process whose particle trajectories form bi-infinite trajectories carrying entropy.
Keywords
Cite
@article{arxiv.1909.04816,
title = {Stationary coalescing walks on the lattice II: Entropy},
author = {Jon Chaika and Arjun Krishnan},
journal= {arXiv preprint arXiv:1909.04816},
year = {2021}
}
Comments
Fixed some typos, included a reference to Hoffman's paper on discrete time totally asymmetric simple exclusion