Arrival of information at a target set in a network
Combinatorics
2025-04-01 v3 Mathematical Physics
Dynamical Systems
math.MP
Abstract
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.)
Keywords
Cite
@article{arxiv.2406.13033,
title = {Arrival of information at a target set in a network},
author = {Karl Petersen and Ibrahim Salama},
journal= {arXiv preprint arXiv:2406.13033},
year = {2025}
}
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