临界高尔顿-沃森树上线性边增强随机漫步的缩放极限

IF 1.1 3区 数学 Q2 STATISTICS & PROBABILITY
G. Andriopoulos, Eleanor Archer
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引用次数: 0

摘要

我们证明了$\gamma$稳定的临界Galton Watson树上线性边增强随机游动的不变性原理,其中$\gamma \in(1,2]$,并且其中将$x$连接到其父树的边已经重新缩放了一些$\alpha\leq 1$的初始权重$d(\rho,x)^{\alpha}$。这与初始权重的循环制度相对应。然后,我们为极限过程建立了精细的渐近性。在瞬态状态下,我们还给出了离散设置中随机游动位移的上界,表明边缘增强随机游动从不具有正速度,即使初始边缘权重强烈偏离根部。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Scaling limit of linearly edge-reinforced random walks on critical Galton-Watson trees
We prove an invariance principle for linearly edge reinforced random walks on $\gamma$-stable critical Galton-Watson trees, where $\gamma \in (1,2]$ and where the edge joining $x$ to its parent has rescaled initial weight $d(\rho, x)^{\alpha}$ for some $\alpha \leq 1$. This corresponds to the recurrent regime of initial weights. We then establish fine asymptotics for the limit process. In the transient regime, we also give an upper bound on the random walk displacement in the discrete setting, showing that the edge reinforced random walk never has positive speed, even when the initial edge weights are strongly biased away from the root.
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来源期刊
Electronic Journal of Probability
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.
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