The branching Brownian motion seen from its tip
arXiv:1104.3738
Abstract
It has been conjectured since the work of Lalley and Sellke (1987) that the branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. Very recently, it emerged that this can be proved in several different ways (see e.g. Brunet and Derrida, 2010, Arguin et al., 2010, 2011). The structure of this extremal point process turns out to be a Poisson point process with exponential intensity in which each atom has been decorated by an independent copy of an auxiliary point process. The main goal of the present work is to give a complete description of the limit object via an explicit construction of this decoration point process. Another proof and description has been obtained independently by Arguin et al. (2011).
47 pages, 3 figures
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Cited by in corpus (9)
- Extreme local extrema of two-dimensional discrete Gaussian free field
- Branching Brownian motion with selection
- Branching Brownian motion with selection of the N right-most particles: An approximate model
- A note on the rightmost particle in a Fleming-Viot process
- Scaling limit of the path leading to the leftmost particle in a branching random walk
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- The near-critical scaling window for directed polymers on disordered trees
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- An ergodic theorem for the frontier of branching Brownian motion