Y. Morita et al., UNIVERSAL CORRELATIONS IN RANDOM MATRICES AND ONE-DIMENSIONAL PARTICLES WITH LONG-RANGE INTERACTIONS IN A CONFINEMENT POTENTIAL, Physical review. B, Condensed matter, 52(7), 1995, pp. 4716-4719
We study the correlations between eigenvalues of the large random matr
ices by a renormalization group approach. The results strongly support
the universality of the correlations proposed by Brezin and Zee. Then
we apply the results to the ground state of the one-dimensional parti
cles with long-range interactions in a confinement potential. We obtai
n the exact ground state. We also show the existence of a transition s
imilar to a phase separation. Before and after the transition, we obta
in the density-density correlation explicitly. The correlation shows n
ontrivial universal behavior.