Xinxin Chen
Published 2014-02-24Version 1
We consider a branching random walk on the line. Biggins and Kyprianou [6] proved that, in the boundary case, the associated derivative martingale converges almost surly to a finite nonnegative limit, whose law serves as a fixed point of a smoothing transformation (Mandelbrot's cascade). In the present paper, we give a necessary and sufficient condition for the non-triviality of this limit and establish a Kesten-Stigum-like result.
Branching Random Walks, Stable Point Processes and Regular Variation
A short proof of the asymptotic of the minimum of the branching random walk after time $n$
Scaling limit and ageing for branching random walk in Pareto environment
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