Accuracy and range of validity of the Wigner surmise for mixed symmetry classes in random matrix theory

Abstract

Schierenberg et al. [Phys. Rev. E 85, 061130 (2012)] 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 crossover between the Gaussian orthogonal and unitary ensembles by contrasting them with the large-N results that I evaluated using the Nystrom-type 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.