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Large N Asymptotics in Random Matrices

The Riemann–Hilbert Approach
  • Alexander R. ItsEmail author
Chapter
Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

The Hermitian matrix model is defined as the ensemble \(\mathcal{H}_N \) of random Hermitian \({N}\,\times\,{N} \) matrices \({M}\,=\,{(M_{ij})}^{N}_{i,j=1} \) with the probability distribution
$${\mu N({\rm d} {M})}\,=\,\widehat{Z}^{-1}_{N}{\rm exp}(-N\, {\rm Tr}\,V(M)){{\rm d}{M}}.$$
(5.1)

Keywords

Orthogonal Polynomial Random Matrix Random Matrix Theory Hilbert Problem Jump Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics SciencesIndiana University–Purdue University IndianapolisIndianapolisUSA

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