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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.04816
- arXiv:
- arXiv:1909.04816
- Bibcode:
- 2019arXiv190904816C
- Keywords:
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- Mathematics - Probability;
- Mathematics - Dynamical Systems;
- 37A05;
- 37A50;
- 60K35;
- 60K37
- E-Print:
- Fixed some typos, included a reference to Hoffman's paper on discrete time totally asymmetric simple exclusion