Subadditivity, Generalized Products of Random Matrices and Operations Research
Joel E. Cohen · SIAM Review · 1988
An elementary theorem on subadditive sequences provides the key to a far-reaching theory of subadditive processes. One important instance of this theory is the limit theory for products of stationary random matrices. This paper shows that the subadditive inequality that governs the log of the norm of ordinary matrix products also governs other functions of several generalized matrix products. These generalized matrix products are used to calculate minimal cost transportation routes, schedules in manufacturing and minimal and maximal probabilities of multistage processes. The application of subadditive ergodic theory to generalized products of stationary random matrices yields new information about the limiting behavior of generalized products. Exact calculations of the asymptotic behavior are possible in some examples.