Exact joint distributions of any few ordered roots of a class of random matrices

Krishnaiah, P. R.; Waikar, V. B.

doi:10.1016/0047-259x(71)90005-4

Cited by 26 publications

(4 citation statements)

References 6 publications

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“…These involve products of up to [N/2] + 1 incomplete gamma functions. Again, this is consistent with the Pfaffian structure found subsequently in [31,32].…”

Section: Introductionsupporting

confidence: 90%

“…As noted in the Introduction, the Pfaffian structure of F L N (1; x) was first identified in the work of Krishnaiah and collaborators [31,32]. Our starting point is a subsequent refinement of this early work due to Chiani [6].…”

Section: Pfaffian Form Of Fmentioning

confidence: 87%

“…For this the difficulty to be overcome is the requirement to involve the analogue of (2.18) for r + 1/2 a non-negative integer in successive integrations. In §3.3 a second approach will be considered, which involves making use of the Pfaffian structure associated with f L N (1; x) in the case β = 1 as first identified by Krishnaiah and collaborators [31,32]. Important here will be the more recent refinement of the associated formulas due to Chiani [6].…”

Section: The Fixed Trace Variantmentioning

confidence: 99%

“…These involve products of up to [N/2] + 1 incomplete beta functions. Soon after an explanation for such functional forms, in the context of an overarching Pfaffian structure, were obtained in the work of Krishnaiah and collaborators [31,32]. These works used the method of integration over alternate variables, as introduced into random matrix theory by Mehta [38].…”

Section: Introductionmentioning

confidence: 99%

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Large deviation eigenvalue density for the soft edge Laguerre and Jacobi β-ensembles

Forrester¹

2012

J. Phys. A: Math. Theor.

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We analyze the eigenvalue density for the Laguerre and Jacobi β-ensembles in the cases that the corresponding exponents are extensive. In particular, we obtain the asymptotic expansion up to terms o(1), in the large deviation regime outside the limiting interval of support. As found in recent studies of the large deviation density for the Gaussian β-ensemble, and Laguerre β-ensemble with fixed exponent, there is a scaling from this asymptotic expansion to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge.

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“…These involve products of up to [N/2] + 1 incomplete gamma functions. Again, this is consistent with the Pfaffian structure found subsequently in [31,32].…”

Section: Introductionsupporting

confidence: 90%