D. Goldstein, Holon Institute of Technology, Holon 58102, Israel; email: dmitryg@hit.ac.il

I. Goldstein, Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel; email: ilyago@bgu.ac.il

Abstract/Résumé:

We prove certain probabilistic inequalities for long matrix products generated by a pair of \(2\times 2\) matrices. Our main tool is the so-called Goldstein-Schlag avalanche principle.

Nous prouvons certaines inégalités probabilistes concernant les longs produits de matrices générés par une paire de matrices \(2\times 2\). Notre objectif principal concerne le principe d’avalanche, énoncé par Goldstein et Schlag.

Keywords: avalanche principle, deviation probabilities

AMS Subject Classification: Large deviations 60F10

PDF(click to download): The Avalanche Principle and Some Deviation Probabilities

D. Goldstein, Holon Institute of Technology, Holon 58102, Israel; email: dmitryg@hit.ac.il

I. Goldstein, Department of Mathematics, Ben-Gurion University, P. O. Box 653 Beer-Sheva 84105, Israel; email: ilyago@bgu.ac.il

Abstract/Résumé:

The averaged joint spectral radius (AJSR) is defined. By using the avalanche principle we develop an effective algorithm to compute the averaged joint spectral radius for a pair of \(2\times2\) matrices.

Nous introduisons la notion de rayon spectral moyen d’un ensemble fini de matrices. En utilisant le principe d’avalanche, nous développons un algorithme efficace pour calculer le rayon spectral moyen d’une paire de matrices de tailles \(2\times2\).

Keywords: avalanche principle, dilation equation, joint spectral radius

AMS Subject Classification: Eigenvalues; singular values; and eigenvectors 15A18

PDF(click to download): The Avalanche Principle: from Joint to Averaged Joint Spectral Radius