This study addresses the sintering mechanism of Pt nanoparticles dispersed on a planar, amorphous Al2O3 support as a model system for a catalyst for automotive exhaust abatement. By means of in situ transmission electron microscopy (TEM), the model catalyst was monitored during the exposure to 10 mbar air at 650 degrees C. Time-resolved image series unequivocally reveal that the sintering of Pt nanoparticles was mediated by an Ostwald ripening process. A statistical analysis of an ensemble of Pt nanoparticles shows that the particle size distributions change shape from an initial Gaussian distribution via a log-normal distribution to a Lifshitz-Slyozov-Wagner (LSW) distribution. Furthermore, the time-dependency of the ensemble-averaged particle size and particle density is determined. A mean field kinetic description captures the main trends in the observed behavior. However, at the individual nanoparticle level, deviations from the model are observed suggesting in part that the local environment influences the atom exchange process.