Slower deviations of the branching Brownian motion and of branching random walks
arXiv:1705.02277 · doi:10.1088/1751-8121/aa7f98
Abstract
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.
13 pages and 1 figure