瞬态树上高斯自由场的水平集渗透

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2016-06-08 DOI:10.1214/16-AIHP799

Angelo Abacherli, A. Sznitman

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引用次数: 20

摘要

我们研究了瞬态树上高斯自由场的水平集渗透，例如在非消光条件下的超临界高尔顿-沃森树上。最近发展的dynkin型同构定理提供了与随机交错空集渗透的比较，这在树的情况下更容易处理。如果$h_*$和$u_*$分别表示高斯自由场的水平集渗透和随机交错空集的水平集渗透的(非负)临界值，我们在这里表明$h_* 0$。

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Level-set percolation for the Gaussian free field on a transient tree

We investigate level-set percolation of the Gaussian free field on transient trees, for instance on super-critical Galton-Watson trees conditioned on non-extinction. Recently developed Dynkin-type isomorphism theorems provide a comparison with percolation of the vacant set of random interlacements, which is more tractable in the case of trees. If $h_*$ and $u_*$ denote the respective (non-negative) critical values of level-set percolation of the Gaussian free field and of the vacant set of random interlacements, we show here that $h_* 0$.

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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.