We have shown recently how to calculate the large deviation function of the position $X_{ \max}(t) $ of the right most particle of a branching Brownian motion at time $t$. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of $X_{ \max}(t)$ has, asymptotically in time, a prefactor characterized by non trivial power law.
Categories: math-ph cond-mat.stat-mech math.MP math.PR