Markov fields over countable partially ordered sets : extrema and splitting / I. V. Evstigneev, P. E. Greenwood.

Format:

Book

Author/Creator:

Evstigneev, I. V., author.

Greenwood, P. E., 1937- author.

Series:

Memoirs of the American Mathematical Society ; Volume 112, Number 537.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 112, Number 537

Language:

English

Subjects (All):

Markov random fields.

Partially ordered sets.

Physical Description:

1 online resource (113 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island, United States : American Mathematical Society, 1994.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Introduction""; ""1. Splitting lemma""; ""2. Honest random sets""; ""3. Splitting random sets. Constructions of splitting random elements""; ""4. Markov systems and their transformations""; ""5. Shift invariance""; ""6. Some special partially ordered sets and Markov fields""; ""7. Ferry problem""; ""8. The linearly ordered case""; ""9. Fibres""; ""10. Cracks and splitting random elements""; ""11. Transformations of fields indexed by contours""; ""12. Bibliographical notes""; ""References""

Notes:

"November 1994, Volume 112, Number 537 (first of 4 numbers)"--Cover.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0116-9