The branching Brownian motion seen from its tip

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Abstract
Very recently, Arguin et al. have proved the conjecture (which can be found in the work of Lalley and Sellke) that the branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. The main goal of the present work is to give a complete description of the limit object and an alternative proof of the convergence. As conjectured by Brunet and Derrida and proved by Arguin et al., the structure of this extremal point process turns out to be a certain Poisson point process with exponential intensity in which each atom has been decorated by an independent copy of an auxiliary point process. Here, we give an explicit construction of this decoration point process.

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