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History – an overview. (English) Zbl 1390.82005
Schehr, Grégory (ed.) et al., Stochastic processes and random matrices. Lecture notes of the Les Houches summer school. Volume 104, Les Houches, France, July 6–31, 2015. Oxford: Oxford University Press (ISBN 978-0-19-879731-9/hbk). 1-25 (2017).
Summary: When asked to write an overview over the history of random matrix theory (RMT), we faced the difficulty that in the past 20 years RMT has experienced very rapid development. As witnessed by the table of contents of this book, RMT has expanded into a number of areas of physics and mathematics. It has turned out to be impossible to account for this development in the space of the 20 or so pages allocated to us. We decided to focus attention on the first four decades of the history of RMT, and to follow only some lines of development until recent times. Our choice was determined by personal preference and subject knowledge. We have omitted, for instance, the connections between RMT and low-energy field theory, those between RMT and integrability, works on extreme-value statistics, and applications of RMT to wireless communication and to stock-market data. For our reconstruction of the historical line of development, we have only used published literature on the subject.
For the entire collection see [Zbl 1380.60005].
82-03 History of statistical mechanics
15-03 History of linear algebra
01A60 History of mathematics in the 20th century
01A61 History of mathematics in the 21st century
15B52 Random matrices (algebraic aspects)
60B20 Random matrices (probabilistic aspects)
81V35 Nuclear physics
81V70 Many-body theory; quantum Hall effect
81T60 Supersymmetric field theories in quantum mechanics
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82C22 Interacting particle systems in time-dependent statistical mechanics
81Q50 Quantum chaos
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