Singular linear statistics of the Laguerre Unitary Ensemble and Painlevé III (${\mathrm{P}}_{\mathrm{III}}$): Double scaling analysis

Min Chen, Yang Chen

We continue with the study of the Hankel determinant, $$D_n(t,\alpha ):=\det {\left({\int }_0^{\infty }{x}^{j+k}w(x;t,\alpha )dx\right)}_{j,k=0}^{n-1},$$ generated by singularly perturbed Laguer…