On the entropy of a two step random Fibonacci substitution (Q280510)

Summary: We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, \(\mathsf a\mapsto\mathsf{baa}\) and \(\mathsf b\mapsto\mathsf{ab}\), with probability \(p\), and \(\mathsf b\mapsto\mathsf{ba}\), with probability \(1-p\) for \(0<p<1\), and where the random rule is applied each time it acts on \(\mathsf a\) . We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value.