Assuming that small crystallites can perform noninteracting random walks on a substrate, one may calculate the expected rate of collisions between them and the rate of decrease of their numbers. Comparison with experimental results for gold on potassium chloride at temperatures less than 150°C (for which coalescence is not observed despite large root mean square displacements) indicates either that those crystallites do not diffuse as entities or that coalescences are inhibited. It is suggested that inhibition be due to elastic interactions, electrostatic interactions, or impurity effects.