High points of branching Brownian motion and McKean’s Martingale in the Bovier-Hartung extremal process
High points of branching Brownian motion and McKean’s Martingale in the Bovier-Hartung extremal process
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Bovier-Hartung 极值过程中的分支布朗运动和 McKean 鞅的高点
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Marius Schmidt
中科院分区：
文献类型：
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作者：
C. Glenz;N. Kistler;Marius Schmidt
它已被证明是由Bovier和Hartung [选举。J. Probab. 19（2014）]，在弱相关区域中的变速分支布朗运动（BBM）的最大值收敛于随机移位的Gumbel分布。随机移动由McKean鞅的几乎必然极限给出，并捕获了系统的早期演化。因此，在Bovier-Hartung极值过程中，McKean鞅起着与经典BBM中的导数鞅相似的作用。在这篇文章中，我们提供了另一种解释的McKean鞅的大数定律的高点BBM，即粒子的谎言在一个宏观距离的边缘。在这样的尺度下，“类麦基恩鞅”自然会出现在所有属于BBM普适类的模型中。
It has been proved by Bovier & Hartung [ Elect. J. Probab. 19 (2014)] that the maximum of a variable-speed branching Brownian motion (BBM) in the weak correlation regime converges to a randomly shifted Gumbel distribution. The random shift is given by the almost sure limit of McKean’s martingale, and captures the early evolution of the system. In the Bovier-Hartung extremal process, McKean’s martingale thus plays a role which parallels that of the derivative martingale in the classical BBM. In this note, we provide an alternative interpretation of McKean’s martingale in terms of a law of large numbers for high-points of BBM, i.e. particles which lie at a macroscopic distance from the edge. At such scales, ‘McKean-like martingales’ are naturally expected to arise in all models belonging to the BBM-universality class.
影响因子：
3
作者：
Arguin, Louis-Pierre;Belius, David;Soundararajan, Kannan
通讯作者：
Soundararajan, Kannan