The lowest eigenvalue of Jacobi random matrix ensembles and Painleve VI

NC Snaith, JP Keating, Duenez E., Huynh D. K., Miller S. J.

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)

Abstract

We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painlevé VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painlevé VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.
Translated title of the contributionThe lowest eigenvalue of Jacobi random matrix ensembles and Painleve VI
Original languageEnglish
Pages (from-to)405204 - 405230
Number of pages27
JournalJournal of Physics A: Mathematical and Theoretical
Volume43, number 40
DOIs
Publication statusPublished - Oct 2010

Bibliographical note

Publisher: IOP

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