Edge Scaling of the β-Jacobi Ensemble

We study the scaling limit of the spectrum of the β -Jacobi ensemble at the soft edge and hard edge for general values of β . We show that the limiting point processes correspond respectively to the stochastic Airy and Bessel point processes introduced in Ramírez et al. (J. Am. Math. Soc. 24(4):919–...

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Veröffentlicht in:	Journal of statistical physics 2012-12, Vol.149 (6), p.1136-1160
Hauptverfasser:	Holcomb, Diane, Moreno Flores, Gregorio R.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical
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Beschreibung
Zusammenfassung:	We study the scaling limit of the spectrum of the β -Jacobi ensemble at the soft edge and hard edge for general values of β . We show that the limiting point processes correspond respectively to the stochastic Airy and Bessel point processes introduced in Ramírez et al. (J. Am. Math. Soc. 24(4):919–944, 2011 ) and Ramírez and Rider (Commun. Math. Phys. 288(3):887–906, 2009 ).
ISSN:	0022-4715 1572-9613
DOI:	10.1007/s10955-012-0634-3