The Annals of Applied Probability

Large Deviations of Products of Random Topical Operators

Fergal Toomey

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A topical operator on $\mathbb{R}^d$ is one which is isotone and homogeneous. Let ${A(n) : n \geq 1}$ be a sequence of i.i.d. random topical operators such that the projective radius of $A(n) \dots A(1)$ is almost surely bounded for large $n$. If ${x(n) : n \geq 1}$, is a sequence of vectors given by $x(n) = A(n) \dots A(1)x_0$, for some fixed initial condition $x_0$, then the sequence ${x(n)/n : n \geq 1}$ satisfies a weak large deviation principle. As corollaries of this result we obtain large deviation principles for products of certain random aperiodic max-plus and min-plus matrix operators and for products of certain random aperiodic nonnegative matrix operators.

Article information

Ann. Appl. Probab. Volume 12, Number 1 (2002), 317-333.

First available in Project Euclid: 12 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 47H40: Random operators [See also 47B80, 60H25] 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces

Topical operators discrete event systems max-plus algebra nonnegative matrices large deviations


Toomey, Fergal. Large Deviations of Products of Random Topical Operators. Ann. Appl. Probab. 12 (2002), no. 1, 317--333. doi:10.1214/aoap/1015961166.

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