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## On the Entropy of a Family of Random Substitutions

### Abstract

The generalised random Fibonacci chain is a stochastic extension of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 1^i01^{m-i}$ with probability $p_i$, where $p_i\geq 0$ with $\sum_{i=0}^m p_i=1$, and where the random rule is applied each time it acts on a 1. We show that the topological entropy of this object is given by the growth rate of the set of inflated generalised random Fibonacci words.Comment: A more appropriate tile and minor misprints corrected, compared to the previous versio

Topics: Mathematics - Combinatorics, Mathematics - Dynamical Systems, 68R15, 05A16, 37B10
Year: 2012
DOI identifier: 10.1007/s00605-012-0401-1
OAI identifier: oai:arXiv.org:1103.4777