分支布朗运动在两个温度下的重叠分布

IF 1.1 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-01-01 DOI:10.1214/22-ejp841

Benjamin Bonnefont

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引用次数: 0

摘要

我们研究了分支布朗运动在两个温度下在吉布斯测度下选择的两个粒子的重叠分布。我们首先使用Bovier和Hartung[8]获得的极值过程的扩展收敛性来证明重叠分布的收敛性。然后，我们证明了在不同温度下选择的两个点的平均重叠严格小于德里达的随机能量模型。最后一个结果的证明是通过Aïdékon、Berestycki、Brunet和Shi[1]对装饰点过程的描述实现的。据我们所知，这是第一次使用这种描述。关键词——分支布朗运动，吉布斯测度，重叠分布，随机能量模型。

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The overlap distribution at two temperatures for the branching Brownian motion

We study the overlap distribution of two particles chosen under the Gibbs measure at two temperatures for the branching Brownian motion. We first prove the convergence of the overlap distribution using the extended convergence of the extremal process obtained by Bovier and Hartung [8]. We then prove that the mean overlap of two points chosen at different temperatures is strictly smaller than in Derrida’s random energy model. The proof of this last result is achieved with the description of the decoration point process obtained by Aïdékon, Berestycki, Brunet and Shi [1]. To our knowledge, it is the first time that this description is being used. Keywords— Branching Brownian motion, Gibbs measure, overlap distribution, random energy model.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.