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We use a large dataset of approximately 1500 physicists employed by the Centre National de la Recherche Scientifique (CNRS) in France to investigate the role of cumulative advantage in their publication career. Measuring output by time series of the number of publications and the number of cite-weighted publications for each physicist, we find that the simple stylized facts predicted by cumulative advantage hold only weakly for these physicists. However, regressions with fixed effects, life cycle effects, and past productivity provide strong evidence that cumulative advantage matters for future productivity. In future work, we plan to compare this sample with those from other countries that have different systems for the conduct of scientific research