Title: Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting (Memoirs of the American Mathematical Society)
Publisher: Amer Mathematical Society
Publication Date: 1994
Language: English
ISBN 10: 0821825976
ISBN 13: 9780821825976
Binding: Paperback
Condition: Good
Dust Jacket Condition: No Jacket
Weight: 0.45 pounds

About this title

Synopsis

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 self-contained and accessible book will prove useful in the many scientific areas where random field models are appearing.

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