Data-adaptive unfolding of non-standard random-matrix spectra: cross-over of long-range correlation statistics

Recently, a model-free and data-adaptive unfolding method, based on normal-mode analysis, was proposed and demonstrated for standard Gaussian ensembles of Random Matrix Theory (RMT). Here, the method is applied to a sparse matrix ensemble and to the $\nu-$Hermite ensemble. In correspondence with known results, level fluctuations are obtained that exhibit a cross-over between soft and rigid behaviour, whereas fluctuations of standard RMT ensembles are scale invariant. Possible artefacts introduced by standard unfolding techniques are avoided. Ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes and allow to characterize the ergodicity of the ensemble under study.