Normalized image of a vector by an infinite product of nonnegative matrices

Abstract

A sofic measure is the image of a Markov probability measure by a continuous morphism, and can be represented by means of products of matrices $A_n$ that belong to a finite set of nonnegative matrices. To prove that the multifractal formalism holds for such a measure, it is necessary to know whenever the sequence $n\mapsto \frac{A_1\cdots A_{n}v}{\Vert A_1\cdots A_{n}v\Vert }$ converges when $v$ is a positive vector. We give a sufficient condition for this convergence, that we use for the study of one Bernoulli convolution.

19 pages

References in corpus (2)

• Lyapunov spectrum of asymptotically sub-additive potentials
• Can an infinite left-product of nonnegative matrices be expressed in terms of infinite left-products of stochastic ones?