Abstract
The following paper, first written in 1974, was never published other than
as part of an internal research series. Its lack of publication is unrelated
to the merits of the paper and the paper is of current importance by virtue
of its relation to the relaxation time. A systematic discussion is provided
of the approach of a finite Markov chain to ergodicity by proving the
monotonicity of an important set of norms, each measures of egodicity,
whether or not time reversibility is present. The paper is of particular
interest because the discussion of the relaxation time of a finite Markov
chain [2] has only been clean for time reversible chains, a small subset of
the chains of interest. This restriction is not present here. Indeed, a new
relaxation time quoted quantifies the relaxation time for all finite ergodic
chains (cf. the discussion of