Random fields and geometry
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in w...
Guardat en:
| Autors principals: | , |
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| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2007. |
| Col·lecció: | Springer Monographs in Mathematics
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| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 444 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Random fields and geometry, Robert J. Adler, Jonathan E. Taylor, 2007, New York, Springer, 1 volume (xvii-448 pages), Springer monographs in mathematics, 978-0-387-48112-8 • Random Fields and Geometry, Texte imprimé, 9780387564470 • Random fields and geometry, Robert J. Adler, Jonathan E. Taylor, New York, Springer, 2010, 1 vol. (XVI, 448 p., Springer monographs in mathematics, 978-1-4419-2369-1 • Random fields and geometry, Robert J. Adler, Jonathan E. Taylor, 2007, New York, Springer, 1 volume (xvii-448 pages), Springer monographs in mathematics, 978-0-387-48112-8 |
| Sumari: | This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. The three parts to the monograph are quite distinct. Part I presents a user-friendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, and to give some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, self-contained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics |
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| Descripció de l’ítem: | L'impression du document génère 444 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9780387481166 |
| ISSN: | 2196-9922 |
| Accés: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |