Asymptotics of Muttalib–Borodin determinants with Fisher–Hartwig singularities

Muttalib–Borodin determinants are generalizations of Hankel and depend on a parameter $$\theta >0$$ . In this paper, we obtain large n asymptotics for $$n \times n$$ whose weight possesses an arbitrary number Fisher–Hartwig singularities. As corollary, the expectation variance real imaginary parts logarithm underlying characteristic polynomial, several central limit theorems, some global bulk rigidity upper bounds. Our results valid all > 0$$