不带XlogX条件的高尔顿-沃森树的均匀测度的豪斯多夫维数

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-11-01 DOI:10.1214/19-aihp1031

EF Elie Aidékon

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引用次数: 0

摘要

我们考虑具有有限均值子代分布ν的高尔顿-沃森树。将质量1放在第n代的每个顶点上，取极限n→∞，得到树边界上的一致测度。在E[ν log(ν)] <∞的情况下，这个测度已经得到了很好的研究，已知该测度的Hausdorff维数等于log(m)([3]，[14])。当E[ν log(ν)] =∞时，我们表示维数降为0。这就回答了Lyons、Pemantle和Peres[15]提出的一个问题。

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Hausdorff dimension of the uniform measure of Galton–Watson trees without the XlogX condition

We consider a Galton–Watson tree with offspring distribution ν of finite mean. The uniform measure on the boundary of the tree is obtained by putting mass 1 on each vertex of the n-th generation and taking the limit n → ∞. In the case E[ν log(ν)] < ∞, this measure has been well studied, and it is known that the Hausdorff dimension of the measure is equal to log(m) ([3], [14]). When E[ν log(ν)] = ∞, we show that the dimension drops to 0. This answers a question of Lyons, Pemantle and Peres [15] .

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.