We consider polynomials orthogonal on [0,âˆž) with respect to Laguerre-type weights w(x) = xe, where Î± > âˆ’1 and where Q denotes a polynomial with positive leading coefficient. The main purpose of thisâ€¦ (More)

We consider polynomials that are orthogonal on [âˆ’1, 1] with respect to a modified Jacobi weight (1 âˆ’ x)Î±(1 + x)Î²h(x), with Î±, Î² > âˆ’1 and h real analytic and stricly positive on [âˆ’1, 1]. We obtainâ€¦ (More)

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is describedâ€¦ (More)

We study asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight, which is a weight function with a finite number of algebraic singularitiesâ€¦ (More)

We study unitary random matrix ensembles of the form Zâˆ’1 n,N | detM | 2Î±eâˆ’N TrV dM, where Î± > âˆ’1/2 and V is such that the limiting mean eigenvalue density for n,N â†’ âˆž and n/N â†’ 1 vanishesâ€¦ (More)

We establish universality of local eigenvalue correlations in unitary random matrix ensembles 1 Zn | det M | 2Î± e âˆ’ntr V (M) dM near the origin of the spectrum. If V is even, and if the recurrenceâ€¦ (More)

We establish universality of local eigenvalue correlations in unitary random matrix ensembles 1 Zn |det M |2Î±eâˆ’ntr V dM near the origin of the spectrum. If V is even, and if the recurrenceâ€¦ (More)

We consider unitary random matrix ensembles Z n,s,te âˆ’n tr s,tdM on the space of Hermitian n Ã— n matrices M , where the confining potential Vs,t is such that the limiting mean density of eigenvaluesâ€¦ (More)

It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related toâ€¦ (More)