Modern discrete probability an essential toolkit
Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, conce...
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| Format: | E-Book |
| Sprache: | English |
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Cambridge, United Kingdom ; New York, NY
Cambridge University Press
2024
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| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
55 |
| Online-Zugang: | Volltext |
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| 245 | 1 | 0 | |a Modern discrete probability |b an essential toolkit |c Sébastien Roch, University of Wisconsin-Madison |
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| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics |v 55 | |
| 520 | |a Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering. | ||
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| spelling | Roch, Sébastien Modern discrete probability an essential toolkit Sébastien Roch, University of Wisconsin-Madison Cambridge, United Kingdom ; New York, NY Cambridge University Press 2024 1 Online-Ressource (xvi, 434 Seiten) txt c cr Cambridge series in statistical and probabilistic mathematics 55 Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering. Erscheint auch als Druck-Ausgabe 9781009305112 TUM01 ZDB-20-CTM TUM_PDA_CTM https://doi.org/10.1017/9781009305129 Volltext |
| spellingShingle | Roch, Sébastien Modern discrete probability an essential toolkit |
| title | Modern discrete probability an essential toolkit |
| title_auth | Modern discrete probability an essential toolkit |
| title_exact_search | Modern discrete probability an essential toolkit |
| title_full | Modern discrete probability an essential toolkit Sébastien Roch, University of Wisconsin-Madison |
| title_fullStr | Modern discrete probability an essential toolkit Sébastien Roch, University of Wisconsin-Madison |
| title_full_unstemmed | Modern discrete probability an essential toolkit Sébastien Roch, University of Wisconsin-Madison |
| title_short | Modern discrete probability |
| title_sort | modern discrete probability an essential toolkit |
| title_sub | an essential toolkit |
| url | https://doi.org/10.1017/9781009305129 |
| work_keys_str_mv | AT rochsebastien moderndiscreteprobabilityanessentialtoolkit |