Year: 2019
Type: article
Abstract: We study the top Lyapunov exponents of random products of positive 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.
Source: Nonlinearity
Authors: Natalia Jurga, Ian Morris
Institution: University of Surrey
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Leverhulme Trust
Awards: G382211468, G8526945721
OpenAlex ID: W2921403637