Branching Brownian motion seen from its tip

By Elie Aidékon, J. Berestycki, E. Brunet, Zhan Shi. 2011

187 citations recorded by the source corpus.

It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052–1061, 1987) that 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, A branching random walk seen from the tip, 2010, Poissonian statistics in the extremal process of branching Brownian motion, 2010; Arguin et al., The extremal process of branching Brownian motion, 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. (The extremal process of branching Brownian motion, 2011).

Subfields: Finance, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/5d1e7167634a741c9e23aa4e03890c4c778800fa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Zhan Shi
2. Ofer Zeitouni
3. P. Maillard
4. Jian Ding
5. Thomas Madaule
6. David Belius
7. Bertrand Cloez
8. L. Arguin

In Mathematical Physics

1. Zhan Shi
2. Thomas Madaule
3. David Belius
4. Jian Ding
5. Ofer Zeitouni
6. N. Kistler
7. P. Maillard
8. Joseph Najnudel

In Molecular Biology

1. P. Maillard
2. Thomas Madaule
3. Zhan Shi
4. David Belius
5. N. Kistler
6. Ofer Zeitouni
7. Bertrand Cloez
8. Jian Ding

Citations in the corpus

• Branching random walks (2015, methodology): “See also Gouéré [117] for an analysis based on [27], [28], [29] and [12], and Subag and Zeitouni [225] for a general view of decorated Poisson point processes.”
• Extreme values for two-dimensional discrete Gaussian free field (2012, background): “tructure of the point process of maxima of the BBM was described in great detail, in a series of papers by Arguin, Bovier and Kistler [8, 9, 7] and in a paper by A¨ıd´ekon, Berestycki, Brunet and Shi [4]. These papers describe the limit of the process of extremes of BBM, as a certain Poisson point p”
• Convergence in Law for the Branching Random Walk Seen from Its Tip (2011, methodology): “The second-order problem was recently studied separately by Hu and Shi [15] (a.s fluctuation), and AddarioBerry and Reed [1].”
• A note on stable point processes occurring in branching Brownian motion (2011, methodology): “The decomposition (1.1) was also shown for the branching random walk by Madaule [18], relying on the author’s result.”
• The subleading order of two dimensional cover times (2014, background): “Even more challenging would be the full description of the process of covering; also in this case, the analogy with BBM suggests that regions which are missed the longest form a Poisson cluster process of random intensity [1, 3].”
• Limit theorems for some branching measure-valued processes (2011, methodology): “This model was studied in [1], [4]–[6], [17], and [23].”
• Maximum of a log-correlated Gaussian field (2013, background): “As in the case of the branching Brownian motion, see [6], [7], [8] and [3], our work could also lead to the “genealogy of the extremal particles” which in our context corresponds to their spatial position.”