Format:
1 Online-Ressource (xx, 350 Seiten).
ISBN:
978-1-108-76890-0
Content:
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 The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient.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
Note:
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
Additional Edition:
Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-1-108-48808-2
Language:
English
Subjects:
Mathematics
Keywords:
Big Data
;
Stochastische Matrix
;
Matrizenrechnung
;
Matrizentheorie
;
Stochastische Matrix
DOI:
10.1017/9781108768900
URL:
Volltext
(URL des Erstveröffentlichers)
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