A first course in random matrix theory: for Physicists, Engineers and Data Scientists
The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the re...
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, Australia ; New Dehli, India ; Singapore
Cambridge Universty Press
2020
|
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 FUBA1 UER01 URL des Erstveröffentlichers |
| Zusammenfassung: | The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 12 Nov 2020) Determine matrices -- Wigner ensemble and semi-circle law -- More on Gaussian matrices -- Wishart ensemble and Marcenko-Pastur distribution -- Joint distribution of eigenvalues -- Eigenvalues and Orthogonal polynomials -- The Jacobi ensemble -- Addition of random variables & Brownian motion -- Dyson Brownian motion -- Addition of large random matrices -- Free probabilities -- Free random matrices -- The replica method -- Edge eigenvalues and outliers -- Addition and multiplication : recipes and examples -- Products of many random matrices -- Sample covariance matrices -- Bayesian estimation -- Eigenvector overlaps and rotationally invariant estimators -- Applications to finance |
| Beschreibung: | 1 Online-Ressource (xx, 350 Seiten) |
| ISBN: | 9781108768900 |
| DOI: | 10.1017/9781108768900 |
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Datensatz im Suchindex
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| discipline | Mathematik |
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| id | DE-604.BV047052264 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:08:29Z |
| indexdate | 2024-07-10T09:01:14Z |
| institution | BVB |
| isbn | 9781108768900 |
| language | English |
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| spelling | Potters, Marc 1969- Verfasser (DE-588)129063096 aut A first course in random matrix theory for Physicists, Engineers and Data Scientists Marc Potters (Capital Fund Management, Paris), Jean-Philippe Bouchaud (Capital Fund Management, Paris) Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, Australia ; New Dehli, India ; Singapore Cambridge Universty Press 2020 1 Online-Ressource (xx, 350 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 12 Nov 2020) Determine matrices -- Wigner ensemble and semi-circle law -- More on Gaussian matrices -- Wishart ensemble and Marcenko-Pastur distribution -- Joint distribution of eigenvalues -- Eigenvalues and Orthogonal polynomials -- The Jacobi ensemble -- Addition of random variables & Brownian motion -- Dyson Brownian motion -- Addition of large random matrices -- Free probabilities -- Free random matrices -- The replica method -- Edge eigenvalues and outliers -- Addition and multiplication : recipes and examples -- Products of many random matrices -- Sample covariance matrices -- Bayesian estimation -- Eigenvector overlaps and rotationally invariant estimators -- Applications to finance The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists Random matrices Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Big Data (DE-588)4802620-7 gnd rswk-swf Big Data (DE-588)4802620-7 s Stochastische Matrix (DE-588)4057624-3 s Matrizenrechnung (DE-588)4126963-9 s DE-604 Matrizentheorie (DE-588)4128970-5 s Bouchaud, Jean-Philippe 1962- Verfasser (DE-588)129063053 aut Erscheint auch als Druck-Ausgabe, Hardcover 978-1-108-48808-2 https://doi.org/10.1017/9781108768900 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Potters, Marc 1969- Bouchaud, Jean-Philippe 1962- A first course in random matrix theory for Physicists, Engineers and Data Scientists Random matrices Matrizentheorie (DE-588)4128970-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Stochastische Matrix (DE-588)4057624-3 gnd Big Data (DE-588)4802620-7 gnd |
| subject_GND | (DE-588)4128970-5 (DE-588)4126963-9 (DE-588)4057624-3 (DE-588)4802620-7 |
| title | A first course in random matrix theory for Physicists, Engineers and Data Scientists |
| title_auth | A first course in random matrix theory for Physicists, Engineers and Data Scientists |
| title_exact_search | A first course in random matrix theory for Physicists, Engineers and Data Scientists |
| title_exact_search_txtP | A first course in random matrix theory for Physicists, Engineers and Data Scientists |
| title_full | A first course in random matrix theory for Physicists, Engineers and Data Scientists Marc Potters (Capital Fund Management, Paris), Jean-Philippe Bouchaud (Capital Fund Management, Paris) |
| title_fullStr | A first course in random matrix theory for Physicists, Engineers and Data Scientists Marc Potters (Capital Fund Management, Paris), Jean-Philippe Bouchaud (Capital Fund Management, Paris) |
| title_full_unstemmed | A first course in random matrix theory for Physicists, Engineers and Data Scientists Marc Potters (Capital Fund Management, Paris), Jean-Philippe Bouchaud (Capital Fund Management, Paris) |
| title_short | A first course in random matrix theory |
| title_sort | a first course in random matrix theory for physicists engineers and data scientists |
| title_sub | for Physicists, Engineers and Data Scientists |
| topic | Random matrices Matrizentheorie (DE-588)4128970-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Stochastische Matrix (DE-588)4057624-3 gnd Big Data (DE-588)4802620-7 gnd |
| topic_facet | Random matrices Matrizentheorie Matrizenrechnung Stochastische Matrix Big Data |
| url | https://doi.org/10.1017/9781108768900 |
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