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Cover: 9781107428829 | The Surprising Mathematics of Longest Increasing Subsequences | Romik
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The Surprising Mathematics of Longest Increasing Subsequences
Taschenbuch von Dan Romik
Sprache: Englisch

47,80 €*

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Beschreibung
In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.
In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.
Über den Autor
Dan Romik is Professor of Mathematics at the University of California, Davis.
Zusammenfassung
This book presents for the first time to a graduate-level readership recent groundbreaking developments in probability and combinatorics related to the longest increasing subsequence problem. Its detailed, playful presentation provides a motivating entry to elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians.
Inhaltsverzeichnis
1. Longest increasing subsequences in random permutations; 2. The Baik-Deift-Johansson theorem; 3. Erd¿s-Szekeres permutations and square Young tableaux; 4. The corner growth process: limit shapes; 5. The corner growth process: distributional results; Appendix: Kingman's subadditive ergodic theorem.
Details
Erscheinungsjahr: 2015
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 366
ISBN-13: 9781107428829
ISBN-10: 1107428823
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Romik, Dan
Hersteller: Cambridge University Press
Maße: 229 x 152 x 20 mm
Von/Mit: Dan Romik
Erscheinungsdatum: 05.03.2015
Gewicht: 0,53 kg
preigu-id: 105108393
Über den Autor
Dan Romik is Professor of Mathematics at the University of California, Davis.
Zusammenfassung
This book presents for the first time to a graduate-level readership recent groundbreaking developments in probability and combinatorics related to the longest increasing subsequence problem. Its detailed, playful presentation provides a motivating entry to elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians.
Inhaltsverzeichnis
1. Longest increasing subsequences in random permutations; 2. The Baik-Deift-Johansson theorem; 3. Erd¿s-Szekeres permutations and square Young tableaux; 4. The corner growth process: limit shapes; 5. The corner growth process: distributional results; Appendix: Kingman's subadditive ergodic theorem.
Details
Erscheinungsjahr: 2015
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 366
ISBN-13: 9781107428829
ISBN-10: 1107428823
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Romik, Dan
Hersteller: Cambridge University Press
Maße: 229 x 152 x 20 mm
Von/Mit: Dan Romik
Erscheinungsdatum: 05.03.2015
Gewicht: 0,53 kg
preigu-id: 105108393
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