We study the top Lyapunov exponents of random products of positive [ image ] matrices and obtain an efficient algorithm for its computation. As in the earlier work of Pollicott (2010 Inventiones Math. 181 209-26), the algorithm is based on the Fredholm theory of determinants of trace-class linear operators. In this article we obtain a simpler expression for the approximations which only require calculation of the eigenvalues of finite matrix products and not the eigenvectors. Moreover, we obtain effective bounds on the error term in terms of two explicit constants: a constant which describes how far the set of matrices are from all being column stochastic, and a constant which measures the minimal amount of projective contraction of the positive quadrant under the action of the matrices.
- Pub Date:
- November 2019
- Lyapunov exponent;
- random matrix products;
- transfer operator;
- Mathematics - Dynamical Systems
- Updated definition of constant r, updated examples section, new section on scope for generalising results to higher dimensions, proof of lemma 2.1 corrected