Publikation: The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI
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2010
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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.
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510 Mathematik
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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: 10.1088/1751-8113/43/40/405204BibTex
@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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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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