Wednesday, September 5, 2012

1209.0696 (Shinsuke M. Nishigaki)

Comment on Wigner surmise for mixed symmetry classes in random matrix

Shinsuke M. Nishigaki
Schierenberg-Bruckmann-Wettig [Phys. Rev. E 85, 061130 (2012)] have recently applied the Wigner surmise, i.e. substitution of \infty \times \infty matrices by their 2 \times 2 counterparts for the computation of level spacing distributions, to random matrix ensembles in transition between two universality classes. I examine the accuracy and the range of validity of the surmise for the GOE-GUE crossover, by contrasting them with the large-N results evaluated by myself using the Nystrom method for the Fredholm determinant. The surmised expression at the best-fitting parameter provides a good approximation for 0 \lesssim s \lesssim 2, i.e. the validity range of the original surmise.
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