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Stationary coalescing walks on the lattice II: entropy
- Source :
- Nonlinearity. 34:7045-7063
- Publication Year :
- 2021
- Publisher :
- IOP Publishing, 2021.
-
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.<br />Fixed some typos, included a reference to Hoffman's paper on discrete time totally asymmetric simple exclusion
- Subjects :
- Applied Mathematics
Carry (arithmetic)
Probability (math.PR)
010102 general mathematics
Dimension (graph theory)
Integer lattice
Lattice (group)
General Physics and Astronomy
Statistical and Nonlinear Physics
Dynamical Systems (math.DS)
Translation (geometry)
01 natural sciences
010104 statistics & probability
Entropy (classical thermodynamics)
Positive entropy
FOS: Mathematics
Statistical physics
Mathematics - Dynamical Systems
0101 mathematics
Invariant (mathematics)
Mathematics - Probability
Mathematical Physics
37A05, 37A50, 60K35, 60K37
Mathematics
Subjects
Details
- ISSN :
- 13616544 and 09517715
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- Nonlinearity
- Accession number :
- edsair.doi.dedup.....3dfa9b4ac8f7702d986dde1ba55797db