Slower deviations of the branching Brownian motion and of branching random walks

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

References in corpus (2)

• Spatial Extent of Branching Brownian Motion
• Phenomenological picture of fluctuations in branching random walks

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