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

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

2006-05-23

arxiv.org/abs/math-ph/0605064v1

Journal of Statistical Mechanics: Theory and Experiment P07005 (2006) P07005

Physics

Mathematical Physics

Latex, 34 pages, 5 figures

Scientific paper

10.1088/1742-5468/2006/07/P07005

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 \rho(x)\sim x^{p/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 saw teeth behaviour.

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