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Progress in high-dimensional percolation and random graphs

Author: Markus Heydenreich; Remco van der Hofstad
Publisher: Cham : Springer, 2017.
Series: CRM short courses.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Heydenreich, Markus.
Progress in high-dimensional percolation and random graphs.
Cham : Springer, 2017
(OCoLC)989966513
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Markus Heydenreich; Remco van der Hofstad
ISBN: 9783319624730 3319624733
OCLC Number: 1013823004
Description: 1 online resource
Contents: Preface --
1. Introduction and motivation --
2. Fixing ideas: Percolation on a tree and branching random walk --
3. Uniqueness of the phase transition --
4. Critical exponents and the triangle condition --
5. Proof of triangle condition --
6. The derivation of the lace expansion via inclusion-exclusion --
7. Diagrammatic estimates for the lace expansion --
8. Bootstrap analysis of the lace expansion --
9. Proof that (Se (B= 2 and (Sb (B= 1 under the triangle condition --
10. The non-backtracking lace expansion --
11. Further critical exponents --
12. Kesten's incipient infinite cluster --
13. Finite-size scaling and random graphs --
14. Random walks on percolation clusters --
15. Related results --
16. Further open problems --
Bibliography.
Series Title: CRM short courses.
Responsibility: Markus Heydenreich, Remco van der Hofstad.

Abstract:

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  Read more...

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