  Random matrix products arise in many science and engineering problems. An
efficient evaluation of its growth rate is of great interest to researchers in
diverse fields. In the current paper, we reformulate this problem with a
generating function approach, based on which two analytic methods are proposed
to compute the growth rate. The new formalism is demonstrated in a series of
examples including an Ising model subject to on-site random magnetic fields,
which seems very efficient and easy to implement. Through an extensive
comparison with numerical computation, we see that the analytic results are
valid in a regime of considerable size.
