Memoirs of the American Mathematical Society 1994; 100 pp; softcover Volume: 112 ISBN10: 0821825976 ISBN13: 9780821825976 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 Order Code: MEMO/112/537
 Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. For the most part, the analysis has focused on the study of some important, but special, examples. This work develops general techniques for studying Markov fields on partially ordered sets. The authors introduce random transformations of the index set which preserve the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material. Given the burst of popularity of random fields, this selfcontained and accessible book will prove useful in the many scientific areas where random field models are appearing. Readership Table of Contents  Splitting lemma
 Honest random sets
 Splitting random sets. Constructions of splitting random elements
 Markov systems and their transformations
 Shift invariance
 Some special partially ordered sets and Markov fields
 Ferry problem
 The linearly ordered case
 Fibres
 Cracks and splitting random elements
 Transformations of fields indexed by contours
 Bibliographical notes
 References
