Convexity of the Lyapunov exponent
type: Item
instance of: scholarly article
title: Convexity of the Lyapunov exponent
zbMATH Open document ID: 0972.15015
DOI: 10.1016/S0024-3795(99)00043-9
published in: Linear Algebra and its Applications
publication date: 1999-11-29T00:00:00Z
review text: Let \(\gamma(p)\) be the maximal Lyapunov exponent for an i.i.d. random product of two matrices \(A\) and \(B\) where the factor \(A\) occurs with probability \(p\) and \(B\) occurs with probability 1-p. Under suitable conditions on \(A\) and \(B\) convexity or concavity of \(\gamma\) on \((0,1)\) is proved while general results cannot hold. F.ex. it is not true that \(\gamma\) is convex on \((0,1)\) for \(A\) and \(B\) normal. Typical positive results are: If \(A\) and \(B\) are symmetric positive-semidefinite \(2\times 2\) matrices then \(\gamma\) is convex. If \(A\) is a nonnegative \(2\times 2\) matrix with nonnegative determinant and \(B\) is the transpose of \(A\) then \(\gamma\) is concave on \((0,1)\).
Mathematics Subject Classification ID: 15B52
zbMATH DE Number: 1371390
zbMATH Keywords: convexity
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: random product of two matrices
author: Hans W. Volkmer
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
full work available at URL: s0024-3795(99)00043-9
OpenAlex ID: W2051864871
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description: scientific article; zbMATH DE number 1371390