M V Berry and P Shukla 2009 J. Phys. A: Math. Theor. 42 485102 doi:10.1088/1751-8113/42/48/485102
Spacing distributions for real symmetric 2 × 2 generalized Gaussian ensembles
M V Berry1 and P Shukla2
Show affiliationsFor ensembles of 2 × 2 real symmetric matrices, the normalized spacing distributions P(S) form a family whose parameter space is the unit cube with coordinates determined by the means and variances of the diagonal and off-diagonal elements. The cube contains a variety of spacing distributions that are calculated analytically; they include the Wigner–Poisson transition, distributions with singularities and Gaussians. Unfolding is superfluous for 2 × 2 matrices, but it can be implemented, giving rise to a further variety of spacing distributions, some surprising.
- PACS
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
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- Dates
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Issue 48 (4 December 2009)
Received 11 August 2009
Published 12 November 2009
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Spacing distributions for real symmetric 2 × 2 generalized Gaussian ensembles
M V Berry and P Shukla 2009 J. Phys. A: Math. Theor. 42 485102
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