Restricted Percolation Critical Exponents in High Dimensions
Restricted Percolation Critical Exponents in High Dimensions
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DOI：
10.1002/cpa.21938
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发表时间：
2018-10
影响因子：
3
通讯作者：
S. Chatterjee;Jack Hanson
中科院分区：
文献类型：
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作者：
S. Chatterjee;Jack Hanson
尽管对d大的临界渗流的研究取得了很大进展，但与二维情况不同，对高维分数空间和盒子中临界簇的性质仍然知之甚少。与此密切相关的模型，如临界分支随机游走，给出了相关高维临界指数值的自然表达式;特别是参见Kozma-Nachelor的猜想，即0和（n，n，n，...）在[−n，n]d内连接的概率为n−2 − 2d。
Despite great progress in the study of critical percolation on ℤd for d large, properties of critical clusters in high‐dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions. Closely related models such as critical branching random walk give natural conjectures for the value of the relevant high‐dimensional critical exponents; see in particular the conjecture by Kozma‐Nachmias that the probability that 0 and (n, n, n, …) are connected within [−n, n]d scales as n−2 − 2d.