Universal distribution of random matrix eigenvalues near the 'birth of a cut' transition

Published 17 July 2006 • IOP Publishing Ltd
, , Citation B Eynard J. Stat. Mech. (2006) P07005 DOI 10.1088/1742-5468/2006/07/P07005

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1 Service de Physique Théorique de Saclay, F-91191 Gif-sur-Yvette Cedex, France

Dates

  1. Received 1 June 2006
  2. Accepted 27 June 2006
  3. Published

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1742-5468/2006/07/P07005

Abstract

We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which correspond to rational singularities ρ(x) ∼ xp/q classified by conformal minimal models and integrable hierarchies, this transition shows logarithmic and non-analytical behaviours. There is no critical exponent; instead, the power of N changes in a sawtooth behaviour.

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A commentary on this article has been published by R Flume and A Klitz, 2008 J. Stat. Mech. N10001.

10.1088/1742-5468/2006/07/P07005