Controlled Spin-Flip Systems

Abstract

We introduce a new tool into the study of spin-flip processes, which we call controlled spin-flip systems. For each spin-flip process we define a related class of controlled spin-flip systems. Our main theorem states that bounds on the behavior of a spin-flip process can be obtained by studying the behavior of the related controlled spin-flip system. Since controlled spin-flip systems are in general easier to work with than regular spin-flip processes (they correspond to finite state space Markov processes), our main theorem has applications to some of the important problems concerning spin-flip processes. In particular, we discuss several applications to the uniqueness problem. These include proofs of some new results, as well as new proofs of earlier results.