Free random Levy variables and financial probabilities

We suggest that Free Random Variables, represented here by large random mat rices with spectral Levy disorder, may be relevant for several problems rel ated to the modeling of financial systems. In particular, we consider a fin ancial covariance matrix composed of asymmetric and free random Levy matric es. We derive an algebraic equation for the resolvent and solve it to extra ct the spectral density. The free eigenvalue spectrum is in remarkable agre ement with the one obtained from the covariance matrix of the SP500 financi al market. (C) 2001 Published by Elsevier Science B.V.