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We propose a random matrix modeling for the parametric evolution ofeigenstates. The model is inspired by a large class of quantized chaoticsystems. Its unique feature is having parametric invariance while stillpossessing the non-perturbative crossover that has been discussed by Wigner 50years ago. Of particular interest is the emergence of an additional crossoverto multifractality.Comment: 7 pages, 6 figures, expanded versio

Parametric invariant random matrix model and the emergence of multifractality