The Triangle-Free Process and the Ramsey Number (Record no. 17666)
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| fixed length control field | 04206nam a22004693i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC6176737 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114212.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s1920 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470456566 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470440718 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC6176737 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL6176737 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1151199549 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA164 |
| Item number | .P668 2020 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511/.6 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Pontiveros, Gonzalo Fiz. |
| 245 14 - TITLE STATEMENT | |
| Title | The Triangle-Free Process and the Ramsey Number |
| -- | (3,k) |
| -- | |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 1920. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©1920. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (138 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.263 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- 1.1. Random graph processes -- 1.2. The triangle-free process -- Chapter 2. An overview of the proof -- Chapter 3. Martingale bounds: The line of peril and the line of death -- 3.1. The line of peril and the line of death -- 3.2. A general lemma -- 3.3. The events \X( ), \Y( ), \Z( ) and \Q( ) -- 3.4. Tracking ₑ -- Chapter 4. Tracking everything else -- 4.1. Building sequences -- 4.2. Self-correction -- 4.3. Creating and destroying copies of -- 4.4. Balanced non-tracking graph structures -- 4.5. Bounding the maximum change in *ᵩ( ) -- 4.6. The land before time = -- 4.7. Proof of Theorem 4.1 -- Chapter 5. Tracking ₑ, and mixing in the -graph -- 5.1. Mixing inside open neighbourhoods -- 5.2. Mixing in the whole -graph -- 5.3. Creating and destroying -walks -- 5.4. Self-correction -- 5.5. The Lines of Peril and Death -- Chapter 6. Whirlpools and Lyapunov functions -- 6.1. Whirlpools -- 6.2. Lyapunov functions -- 6.3. The proof of Theorems 2.1, 2.4, 2.5, 2.7 and 2.11 -- Chapter 7. Independent sets and maximum degrees in _{ ,\triangle} -- 7.1. A sketch of the proof -- 7.2. Partitioning the bad events -- 7.3. The events \A( , ) and \A'( , ) -- 7.4. The events \B( , )∩\D( , )^{ } and \B'( , )∩\D( , )^{ } -- 7.5. The events \C( , ) and \C'( , ) -- 7.6. The event \D( , ) -- 7.7. The proof of Propositions 7.1 and 7.2 -- Acknowledgements -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the "diagonal" Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the "off-diagonal" Ramsey numbers R(3,k). In this model, edges of K_n are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted G_n,\triangle . In 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that R(3,k) = \Theta \big ( k^2 / \log k \big ). In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Probability theory and stochastic processes -- Combinatorial probability. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Griffiths, Simon. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Morris, Robert. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Pontiveros, Gonzalo Fiz |
| Title | The Triangle-Free Process and the Ramsey Number |
| -- | (3,k) |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c1920 |
| International Standard Book Number | 9781470440718 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6176737">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6176737</a> |
| Public note | Click to View |
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