The Oxford Handbook of Random Matrix Theory

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ID: 305110
2015
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Abstract
This handbook showcases the major aspects and modern applications of random matrix theory (RMT). It examines the mathematical properties and applications of random matrices and some of the reasons why RMT has been very successful and continues to enjoy great interest among physicists, mathematicians and other scientists. It also discusses methods of solving RMT, basic properties and fundamental objects in RMT, and different models and symmetry classes in RMT. Topics include the use of classical orthogonal polynomials (OP) and skew-OP to solve exactly RMT ensembles with unitary, and orthogonal or symplectic invariance respectively, all at finite matrix size; the supersymmetric and replica methods; determinantal point processes; Painlevé transcendents; the fundamental property of RMT known as universality; RNA folding; two-dimensional quantum gravity; string theory; and the mathematical concept of free random variables. In addition to applications to mathematics and physics, the book considers broader applications to other sciences, including economics, engineering, biology, and complex networks.
Reference Key
openalex_W1813708725 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Gernot Akemann, Jinho Baik, Philippe Di Francesco
Journal Oxford University Press eBooks
Year 2015
DOI
10.1093/oxfordhb/9780198744191.001.0001
URL
https://doi.org/10.1093/oxfordhb/9780198744191.001.0001
Keywords Keywords not found

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