Gap Probability Distribution of Gaussian Unitary Ensembles and Painlevé V Equation

Shengjie Zhang, Shulin Lyu

We consider the Hankel determinant generated by the moments of the even weight function ${\mathrm{e}}^{-x^2}(A+B\hat{I}¸(x^2-a^2)),x\in (-\infty ,+\infty ),a>0,A\ge 0,A+B\ge 0$. It is intimate…