Random matrix ensembles associated with lax matrices.
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an integrable structure permits us to calculate the joint distribution of eigenvalues for these matrices analytically. Spectral statistics of these ensembles are quite unusual and in many cases give rigorously new examples of intermediate statistics.
Université Paris-Sud, LPTMS, UMR8626, Bât. 100, Université Paris-Sud, 91405 Orsay, France.
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Bogomolny
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Giraud
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Schmit