1,655 research outputs found
On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line
We investigate the asymptotics of the determinant of N by N Hankel matrices
generated by Fisher-Hartwig symbols defined on the real line, as N becomes
large. Such objects are natural analogues of Toeplitz determinants generated by
Fisher-Hartwig symbols, and arise in random matrix theory in the investigation
of certain expectations involving random characteristic polynomials. The
reduced density matrices of certain one-dimensional systems of impenetrable
bosons can also be expressed in terms of Hankel determinants of this form.
We focus on the specific cases of scaled Hermite and Laguerre weights. We
compute the asymptotics using a duality formula expressing the N by N Hankel
determinant as a 2|q|-fold integral, where q is a fixed vector, which is valid
when each component of q is natural.We thus verify, for such q, a recent
conjecture of Forrester and Frankel derived using a log-gas argument.Comment: 16 pages. Published version, with new references added, and some
minor errors correcte
Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
For the orthogonal-unitary and symplectic-unitary transitions in random
matrix theory, the general parameter dependent distribution between two sets of
eigenvalues with two different parameter values can be expressed as a
quaternion determinant. For the parameter dependent Gaussian and Laguerre
ensembles the matrix elements of the determinant are expressed in terms of
corresponding skew-orthogonal polynomials, and their limiting value for
infinite matrix dimension are computed in the vicinity of the soft and hard
edges respectively. A connection formula relating the distributions at the hard
and soft edge is obtained, and a universal asymptotic behaviour of the two
point correlation is identified.Comment: 37 pgs., 1fi
Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure
This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ? > ?1, a free parameter N and a shift c<0. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as n tends to infinity
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