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Large \(N\) asymptotics in random matrices. The Riemann-Hilbert approach. (English) Zbl 1248.15030

Harnad, John (ed.), Random matrices, random processes and integrable systems. Berlin: Springer (ISBN 978-1-4419-9513-1/hbk; 978-1-4419-9514-8/ebook). CRM Series in Mathematical Physics, 351-413 (2011).
This contribution lectures on
- the Riemann-Hilbert (RH) representation of the orthogonal polynomials and matrix models,
- the asymptotic analysis of the RH problem as well as the DKMVZ method
- the parametrix at the end points as well as the conclusion of the asymptotic analysis, and
- the critical case as well as the double scaling limit and the second Painlevé equation.
For the entire collection see [Zbl 1215.15002].

MSC:

15B52 Random matrices (algebraic aspects)
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