Progress in High-Dimensional Percolation and Random Graphs

Remco Van Der Hofstad

ISBN 10: 3319624725 / ISBN 13: 9783319624723

Edité par Springer International Publishing, Springer International Publishing, 2017

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader's understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4-9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dimensional percolation. Part III, consisting of Chapters 10-13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14-16, features related models and further open problems, with a focus on the big picture.

N° de réf. du vendeur 9783319624723

Détails bibliographiques

• Titre: Progress in High-Dimensional Percolation and Random Graphs
• Éditeur: Springer International Publishing, Springer International Publishing
• Date de parution: 2017
• Langue: anglais
• ISBN à 10 chiffres: 3319624725
• ISBN à 13 chiffres: 9783319624723
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 22 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 22 millimètres de profondeur
• Poids: 617 grammes

A propos de ce titre

Synopsis

This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader's understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study.

Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4-9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime

nsional percolation. Part III, consisting of Chapters 10-13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14-16, features related models and further open problems, with a focus on the big picture.

À propos de l?auteur

Markus Heydenreich is a professor of Applied Mathematics at Ludwig-Maximilians-Universität München. Professor Heydenreich works in Probability theory, he investigates random spatial structures.

Remco van der Hofstad is a professor in Mathematics at Eindhoven University of Technology and scientific director of Eurandom. He received the Prix Henri Poincaré 2003 jointly with Gordon Slade and the Rollo Davidson Prize in 2007. He works on high-dimensional statistical physics, random graphs as models for complex networks, and applications of probability to related fields such as electrical engineering, computer science and chemistry.