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 $c_0$, predicted by the deterministic theory. We show that for $c_0-c\ll c_0$ 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.
Comment: 7 pages, 6 figures