Markus Heydenreich,Remco van der Hofstad
Progress in High-Dimensional Percolation and Random Graphs
Progress in High-Dimensional Percolation and Random Graphs
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Excellent- More about Progress in High-Dimensional Percolation and Random Graphs
The text presents an engaging exposition of high-dimensional percolation, with exercises and open problems for graduate students and researchers. It covers mean-field critical behavior, recent progress, and related models, with a focus on the big picture.
Format: Hardback
Length: 285 pages
Publication date: 04 December 2017
Publisher: Springer International Publishing AG
High-dimensional percolation is a dynamic and exciting field of study that has gained significant attention in recent years. This text provides a comprehensive and engaging exposition of the subject, aimed at graduate students and researchers who wish to enter the world of high-dimensional percolation. The book is divided into four parts, each containing several chapters. Part I introduces the basic concepts of percolation, including the main results, definitions, and properties. No prior knowledge of percolation is assumed, making it accessible to a wide range of readers. Part II focuses on mean-field critical behavior, discussing the two main techniques used to study this phenomenon: differential inequalities and the lace expansion. These techniques are applied to various models of high-dimensional percolation, providing a thorough understanding of the underlying principles. Part III covers recent progress in high-dimensional percolation, presenting partial proofs and overviews of the proofs. The lace expansion and differential inequalities are central to many of these results, and their discrete analogues are also discussed. Part IV explores related models and further open problems, with a focus on the big picture. The book includes over 90 exercises designed to enhance the readers' understanding of the material, as well as many open problems. It is suitable for advanced courses and seminars, as well as for reference and individual study. Overall, this text is a valuable resource for anyone interested in high-dimensional percolation, and it is likely to inspire future work in this field.
Weight: 618g
Dimension: 244 x 162 x 24 (mm)
ISBN-13: 9783319624723
Edition number: 1st ed. 2017
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