THE CONVERGENCE OF THE EXPLORATION PROCESS FOR CRITICAL PERCOLATION ON THE k-OUT GRAPH

IF 0.5 4区数学 Q3 MATHEMATICS

Osaka Journal of Mathematics Pub Date : 2015-07-01 DOI:10.18910/57663

Y. Ota

引用次数: 0

Abstract

We consider the percolation on the k-out graph Gout(n, k). The critical probability of it is 1 k+ √ k2−k . Similarly to the random graph G(n, p), in a scaling window 1 k+ √ k2−k ( 1 + O(n−1/3) ) , the sequence of sizes of large components rescaled by n−2/3 converges to the excursion lengths of a Brownian motion with some drift. Also, the size of the largest component is O(log n) in the subcritical phase, and O(n) in the supercritical phase. The proof is based on the analysis of the exploration process.

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临界渗流勘探过程在k-OUT图上的收敛性

我们考虑k-out图Gout(n, k)上的渗透。它的临界概率是1k +√k2−k。与随机图G(n, p)类似，在缩放窗口1k +√k2−k (1 + O(n−1/3))中，通过n−2/3重新缩放的大分量的大小序列收敛于具有一定漂移的布朗运动的偏移长度。亚临界相中最大组分的大小为O(log n)，超临界相中最大组分的大小为O(n)。论证是基于对勘探过程的分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.