Some consequences of exchangeability in random-matrix theory

Properties of infinite sequences of exchangeable random variables result di rectly in explicit expressions for calculating asymptotic densities of eige nvalues p(infinity)(lambda) of any ensemble of random matrices H whose dist ribution depends only on tr((HH)-H-dagger), where H-dagger is the Hermitian conjugate of H. For real symmetric matrices and for Hermitian matrices, th e densities p(infinity)(lambda) are constructed by summing up Wigner semici rcles with varying radii and weights as confirmed by Monte Carlo simulation s. Extensions to more general matrix ensembles are also considered. [S1063- 651X(99)09504-5].