  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.
