Convergence of eigenvalues to the support of the limiting measure in   critical $\beta$ matrix models
  We consider the convergence of the eigenvalues to the support of the equilibrium measure in the $\beta$ ensemble models under a critical condition. We show a phase transition phenomenon, namely that, with probability one, all eigenvalues will fall in the support of the limiting spectral measure when $\beta>1$, whereas this fails when $\beta<1$. 
Chenjie Fan, Alice Guionnet, Yuqi Song and Andi Wang
math.PR