On the spectrum of random matrices

A study is made of the dis tr ibut ion of eigenvalues in a ce r ta in ensemble of random par t i c les that contains as a special case the ensemble used by Wlgner to give a s ta t i s t ica l descr ip t ion of the energy levels of heavy nuclei, tt is shown that the dis t r ibut ion function of the e lgenvalues divided by the fac tor N {the o r d e r o~ the mat r i ces ) becomes nonrandom In the limit N ~ ~ and can be found by solving a definite functional equation.