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We study a mean-field version of rank-based models of equity markets such asthe Atlas model introduced by Fernholz in the framework of Stochastic PortfolioTheory. We obtain an asymptotic description of the market when the number ofcompanies grows to infinity. Then, we discuss the long-term capitaldistribution. We recover the Pareto-like shape of capital distribution curvesusually derived from empirical studies, and provide a new description of thephase transition phenomenon observed by Chatterjee and Pal. Finally, we addressthe performance of simple portfolio rules and highlight the influence of thevolatility structure on the growth of portfolios.

Capital distribution and portfolio performance in the mean-field Atlas model