Negative large deviations of the front velocity of N-particle branching Brownian motion

We study negative large deviations of the long-time empirical front velocity in the one-sided N-BBM (N-particle branching Brownian motion) model in one dimension. Employing the macroscopic fluctuation theory, we evaluate the probability density that the front velocity c is smaller than the limiting velocity c₀, predicted by the deterministic theory. We show that for c₀-c c₀ the corresponding rate function $s(c)$ coincides, up to a numerical factor, with the similar rate functions for other front models belonging to the Fisher-Kolmogorov-Petrovsky-Piscounov universality class. For large negative values of c, $s(c)$ approaches a simple bound, obtained under the assumption that the branching is completely suppressed during the whole time.