Free energy expansions of a conditional GinUE and large deviations of the smallest eigenvalue of the LUE

Sung-Soo Byun, Seong-Mi Seo, Meng Yang

We consider a planar Coulomb gas ensemble of size $N$ with the inverse temperature $\beta =2$ and external potential $Q(z)=|z{|}^2-2c\log |z-a|$, where $c>0$ and $a\in \mathbb{C}$. Equiv…