Asymptotics of Hankel determinants with a Laguerre-type or Jacobi-type potential and Fisher-Hartwig singularities

We obtain large n asymptotics of n×n Hankel determinants whose weight has a one-cut regular potential and Fisher-Hartwig singularities. restrict our attention to the case where associated equilibrium measure possesses either one soft edge hard (Laguerre-type) or two edges (Jacobi-type). also present some applications in theory random matrices. In particular, we can deduce from results for partition functions with singularities, central limit theorems, correlations characteristic polynomials, gap probabilities (piecewise constant) thinned Laguerre Jacobi-type ensembles. Finally, mention links topics rigidity Gaussian multiplicative chaos.