The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI

Dueñez, Eduardo; Huynh, Duc K.; Keating, Jon P.; Miller, Steven J.; Snaith, Nina C.

The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI

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Datum

2010

Autor:innen

Dueñez, Eduardo

Huynh, Duc K.

Keating, Jon P.

Miller, Steven J.

Snaith, Nina C.

Publikationstyp

Zeitschriftenartikel

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Journal of Physics A: Mathematical and Theoretical. 2010, 43(40), 405204. ISSN 1751-8113. eISSN 1751-8121. Available under: doi: 10.1088/1751-8113/43/40/405204

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

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ISO 690

DUEÑEZ, Eduardo, Duc K. HUYNH, Jon P. KEATING, Steven J. MILLER, Nina C. SNAITH, 2010. The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI. In: Journal of Physics A: Mathematical and Theoretical. 2010, 43(40), 405204. ISSN 1751-8113. eISSN 1751-8121. Available under: doi: 10.1088/1751-8113/43/40/405204

BibTex

@article{Duenez2010lowes-25391,
  year={2010},
  doi={10.1088/1751-8113/43/40/405204},
  title={The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI},
  number={40},
  volume={43},
  issn={1751-8113},
  journal={Journal of Physics A: Mathematical and Theoretical},
  author={Dueñez, Eduardo and Huynh, Duc K. and Keating, Jon P. and Miller, Steven J. and Snaith, Nina C.},
  note={Article Number: 405204}
}

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