Stationary coalescing walks on the lattice II: entropy

被引:0
作者
Chaika, Jon [1 ]
Krishnan, Arjun [2 ]
机构
[1] Univ Utah, Dept Math, Salt Lake City, UT USA
[2] Univ Rochester, Dept Math, Rochester, NY 14627 USA
关键词
entropy; stationary coalescing walks; bi-infinite trajectories; simple exclusion; BUSEMANN FUNCTIONS; GEODESICS;
D O I
10.1088/1361-6544/ac1162
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:7045 / 7063
页数:19
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