Progress in High-Dimensional Percolation and Random Graphs (Запис № 445232)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04853nam a22006015i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-319-62473-0 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20210118121616.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 171122s2017 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783319624730 |
| -- | 978-3-319-62473-0 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-319-62473-0 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA273.A1-274.9 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA274-274.9 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBT |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT029000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBT |
| Source | thema |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBWL |
| Source | thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.2 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Heydenreich, Markus. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 245 10 - TITLE STATEMENT | |
| Title | Progress in High-Dimensional Percolation and Random Graphs |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Markus Heydenreich, Remco van der Hofstad. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2017. |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2017. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XII, 285 p. 10 illus., 1 illus. in color. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | CRM Short Courses, |
| Міжнародний стандартний серійний номер для назви серії (ISSN) | 2522-5200 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 δ = 2 and β = 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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-dimensiona l 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. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE | |
| Terms governing access | Available to subscribing member institutions only. Доступно лише організаціям членам підписки. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE | |
| Standardized terminology for access restriction | Online access from local network of NaUOA. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE | |
| Standardized terminology for access restriction | Online access with authorization at https://link.springer.com/ |
| 506 ## - RESTRICTIONS ON ACCESS NOTE | |
| Standardized terminology for access restriction | Онлайн-доступ з локальної мережі НаУОА. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE | |
| Standardized terminology for access restriction | Онлайн доступ з авторизацією на https://link.springer.com/ |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Probabilities. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Statistics . |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Probability Theory and Stochastic Processes. |
| -- | http://scigraph.springernature.com/things/product-market-codes/M27004 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. |
| -- | http://scigraph.springernature.com/things/product-market-codes/S17020 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | van der Hofstad, Remco. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783319624723 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783319624747 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783319873213 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | CRM Short Courses, |
| -- | 2522-5200 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-319-62473-0">https://doi.org/10.1007/978-3-319-62473-0</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | ЕКнига |
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