Inhomogeneous Markov Chains and Ergodicity Coefficients: John Hajnal (1924-2008)

In 1958, a paper by John Hajnal, a demographer and mathematical statistician, was fundamental in the revival of the theory of inhomogeneous Markov chains. Hajnal made his contribution by the development of tools for the analysis of weak ergodicity, and proofs of fundamental theorems. This article reviews Hajnal's career, and then focuses on the four topics: 1. ergodicity coefficients and the weak ergodicity theorem; 2. scrambling matrices; 3. the coupling theorem; and 4. non-negative matrix products. Related work by other authors, especially Wolfgang Doeblin, is mentioned in context. Attention is given to some recent surveys and applications of ergodicity coefficients, including the Google matrix.