Painlevé IV, $\sigma -$Form and the Deformed Hermite Unitary Ensembles

Mengkun Zhu, Dan Wang, Yang Chen

We study the Hankel determinant generated by a deformed Hermite weight with one jump $w(z,t,\gamma )=e^{-z^2+tz}|z-t{|}^{\gamma }(A+B\theta (z-t))$, where $A\ge 0$, $A+B\ge 0$, $t\in \text{R}$, $γ>-1…