Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.13033 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909556492206080 |
|---|---|
| author | Petersen, Karl Salama, Ibrahim |
| author_facet | Petersen, Karl Salama, Ibrahim |
| contents | We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the tree is independent of the symbol at the root, and prove that the algorithm succeeds in a bounded number of steps, provided that the dimension of the tree is greater than or equal to the maximum row sum of the transition matrix. (The question was motivated by calculation of topological pressure on trees and is an extension of the idea of primitivity for nonnegative matrices.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arrival of information at a target set in a network Petersen, Karl Salama, Ibrahim Combinatorics Mathematical Physics Dynamical Systems 37B10, 37B40, 05C50, 82B20 We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the tree is independent of the symbol at the root, and prove that the algorithm succeeds in a bounded number of steps, provided that the dimension of the tree is greater than or equal to the maximum row sum of the transition matrix. (The question was motivated by calculation of topological pressure on trees and is an extension of the idea of primitivity for nonnegative matrices.) |
| title | Arrival of information at a target set in a network |
| topic | Combinatorics Mathematical Physics Dynamical Systems 37B10, 37B40, 05C50, 82B20 |
| url | https://arxiv.org/abs/2406.13033 |