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Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities. (English) Zbl 1485.42045

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

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
30E25 Boundary value problems in the complex plane
15B52 Random matrices (algebraic aspects)
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