## The Annals of Applied Probability

### Large Deviations of Products of Random Topical Operators

Fergal Toomey

#### Abstract

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

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

Dates
First available in Project Euclid: 12 March 2002

https://projecteuclid.org/euclid.aoap/1015961166

Digital Object Identifier
doi:10.1214/aoap/1015961166

Mathematical Reviews number (MathSciNet)
MR1890067

Zentralblatt MATH identifier
1073.60027

#### Citation

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

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