Large Deviations of Products of Random Topical Operators

Toomey, F. (1999) Large Deviations of Products of Random Topical Operators. (Preprint)

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Abstract

A topical operator on R^d is one which is isotone and homogeneous. Let {A(n) : n ≥ 1} be a sequence of i.i.d. random topical operators such that A(1) is almost surely bounded for large n. If the projective radius of A(n) {x(n) : n ≥ 1} is a sequence of vectors given by x(n) = A(n)...A(1)x_0, for some fixed initial condition x_0, then the sequence {x(n)/n : n ≥ 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 non-negative matrix operators.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:50
Last Modified: 18 Dec 2022 02:39
URI: https://dair.dias.ie/id/eprint/564

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