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The Branching Brownian Motion (BBM) process consists of particles performing independent Brownian motions in , and each particle creating a new one at rate 1 at its current position. The newborn particles’ increments and branchings are independent of the other particles. The N-BBM process starts with N particles and, at each branching time, the left-most particle is removed so that the total number of particles is N for all times. The N-BBM process has been originally proposed by Maillard, and belongs to a family of processes introduced by Brunet and Derrida. We fix a density with a left boundary , and let the initial particles’ positions be iid continuous random variables with density . We show that the empirical measure associated to the particle positions at a fixed time t converges to an absolutely continuous measure with density as . The limit is solution of a …