Physics – Mathematical Physics
Scientific paper
2004-11-04
J. Math. Phys., 46, 043516 (2005)
Physics
Mathematical Physics
16 pages. Published version, with new references added, and some minor errors corrected
Scientific paper
10.1063/1.1867981
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.
No associations
LandOfFree
On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-278516