We present a theoretical study of the interaction of low density lipoprotein (LDL) receptors with coated pits. From published experiments we estimate that the forward rate constant, k+, for the binding of a LDL receptor to a coated pit on a human fibroblast at 37 degrees C is greater than or equal to 3 X 10(-10) cm2/sec, and the mean time an LDL receptor spends on the cell surface before being captured by a coated pit, tc, is less than or equal to 1.8 min. If, when an LDL receptor enters, it remains within the coated pit until the coated pit pinches off to form a coated vesicle, then k+ = 3 X 10(-10) cm2/sec and tc = 1.8 min. We derive expressions for the diffusion limit of k+ and tc when particles (LDL receptors) diffuse in two dimensions until they hit and are absorbed by circular absorbers (coated pits) that have finite lifetimes. The absorbers appear and disappear at equal rates so that their concentration remains constant. We use these expressions to show that a diffusion limit of k+ = 3 X 10(-10) cm2/ sec would be obtained if D, the diffusion coefficient for an LDL receptor on a human fibroblast at 37 degrees C equaled 3.3 X 10(-11) cm2/sec. Because this value is in agreement with the experimentally determined value for D, we conclude that random insertion of LDL receptors into the plasma membrane, followed by pure diffusional motion of LDL receptors on the cell surface until they are irreversibly absorbed in coated pits, is consistent with experiment.