We present a theoretical model that allows us to describe the polariton dynamics in a semiconductor microcavity at large densities, for the case of nonresonant excitation. Exciton-polariton scattering from a thermalized exciton reservoir is identified as the main mechanism for relaxation into the lower polariton states. A maximum in the polariton distribution that shifts towards lower energies with increasing pump power or temperature is shown, in agreement with recent experiments. Above a critical pump power, macroscopic occupancies (5x10(4)) can be achieved in the lowest-energy polariton state. Our model predicts the possibility of Bose-Einstein condensation of polaritons, driven by exciton-polariton interaction, at densities well below the saturation density for CdTe microcavities
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