The Avalanche Principle and Some Deviation Probabilities

C. R. Math. Rep. Acad. Sci. Canada Vol. 32 (1) 2010, pp. 13–18
(Received: 2009-09-09 )

D. Goldstein, Holon Institute of Technology, Holon 58102, Israel; email:

I. Goldstein, Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel; email:


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

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