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) ~ 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 sawtooth behaviour.

Key words: conformal field theory; matrix models

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

E-print number: math-ph/0605064
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Received 1 June 2006, accepted for publication 27 June 2006
Published 17 July 2006