Relaxation rate distributions for supercooled liquids

The mode-coupling theory for the evolution of glassy dynamics in simple liq uids yields correlation functions that, outside the transient regime, can b e written as a superposition of relaxators with a broad distribution of rel axation rates. The known asymptotic laws for the dynamics near an ideal gla ss transition imply corresponding laws for the rate distribution. We calcul ate the rate distributions for a hard-sphere liquid and compare them to the leading and next-to-leading asymptotic formulas.