On ergodic properties of homogeneous Markov chains

In this paper we continue our investigations initiated in [1]. Namely, we study the spectrum of Kolmogorov matrices with at least one column separated from zero. It is shown that $\lambda=0$ is an eigenvalue with multiplicity 1, while the rest of the spectrum is separated from zero. Therefore, a Markov process generated by such a matrix converges to its uniquely defined final distribution exponentially fast. We give an explicit estimate for the rate of this convergence.