Large Deviations of Products of Random Topical Operators

A topical operator on Rd is one which is isotone and homogeneous. Let A(n):n.1 be a sequence of i.i.d. random topical operators such that the projective radius of A(n).A(1) is almost surely bounded for large n. If x(n):n.1, is a sequence of vectors given by x(n)=A(n).A(1)x0, for some fixed initial condition x0, 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 nonnegative matrix operators.