Stationary coalescing walks on the lattice II: entropy. (11th October 2021)

• Record Type: Journal Article
• Authors: Chaika, Jon; Krishnan, Arjun
• Is Part Of: Nonlinearity. Volume 34:Number 10(2021)
• Page Start: 7045
• Page End: 7063
• Publication Date: 2021-10-11
• Subjects: entropy -- stationary coalescing walks -- bi-infinite trajectories -- simple exclusion; 37A05 -- 37A50 -- 60K35 -- 60K37; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac1162
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This paper is a sequel to Chaika and Krishnan, 2016. 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.