  Completely simple semigroups arise as the support of limiting measures of
random walks on semigroups. Such a limiting measure is supported on the kernel
of the semigroup. Forming tensor powers of the random walk leads to a hierarchy
of the limiting kernels. Tensor squares lead to quantum observables on the
kernel. Recall that zeons are bosons modulo the basis elements squaring to
zero. Using zeon powers leads naturally to quantum observables which reveal the
structure of the kernel. Thus asymptotic information about the random walk is
related to algebraic properties of the zeon powers of the random walk.

Rings and Algebras;Functional Analysis;Probability;Representation Theory