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With the first edition out of print we decided to arrange for republi cation of Denumerrible Markov Ohains with additional bibliographic material The new edition contains a section Additional Notes that indicates some of the developments in Markov chain theory over the last ten years As in the first edition and for the same reasons we have resisted the temptation to follow the theory in directions that deal with uncountable state spaces or continuous time A section entitled Additional References complements the Additional Notes J W Pitman pointed out an error in Theorem 953 of the first edition which we have corrected More detail about the correction appears in the Additional Notes Aside from this change we have left intact the text of the first eleven chapters The second edition contains a twelfth chapter written by David Griffeath on Markov random fields We are grateful to Ted Cox for his help in preparing this material Notes for the chapter appear in the section Additional Notes JGK JLS AWK
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