An ergodic theorem for the extremal process of branching Brownian motion
Probability
2012-09-27 v1
Abstract
In a previous paper, the authors proved a conjecture of Lalley and Sellke that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a Gumbel distribution. The result is extended here to the entire system of particles that are extremal, i.e. close to the maximum. Namely, it is proved that the distribution of extremal particles under time-average converges to a Poisson cluster process.
Keywords
Cite
@article{arxiv.1209.6027,
title = {An ergodic theorem for the extremal process of branching Brownian motion},
author = {Louis-Pierre Arguin and Anton Bovier and Nicola Kistler},
journal= {arXiv preprint arXiv:1209.6027},
year = {2012}
}
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14 pages