eBook ISBN:  9781470401160 
Product Code:  MEMO/112/537.E 
List Price:  $40.00 
MAA Member Price:  $36.00 
AMS Member Price:  $24.00 
eBook ISBN:  9781470401160 
Product Code:  MEMO/112/537.E 
List Price:  $40.00 
MAA Member Price:  $36.00 
AMS Member Price:  $24.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 112; 1994; 100 ppMSC: Primary 60
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

Chapters

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


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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.

Chapters

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