图的随机子树模型

IF 1.3 Q2 STATISTICS & PROBABILITY
Luis Fredes, Jean-Francois Marckert
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引用次数: 1

摘要

考虑一个有N=|V|个顶点的连通图G=(E,V)。本文的主要目的是探讨对于n≤n(生成树的情况对应于n= n,在文献中已经有深入的研究)的n个节点的G的子树的均匀抽样问题。对于一般连通图G和任意n≤n,我们给出了新的使用马尔可夫链的渐近精确模拟方法。我们强调了具有n个节点的Z2的一致子树的情况,包含原点(0,0),对此Schramm提出了几个问题。我们制作图片、统计数据和一些猜想。本文的第二个目的是研究图的随机子树的其他模型,其中包括DLA模型、第一通道渗透模型、均匀生成树和最小生成树。我们还提供了新的模型,一些统计数据和一些猜想。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Models of random subtrees of a graph
Consider a connected graph G=(E,V) with N=|V| vertices. The main purpose of this paper is to explore the question of uniform sampling of a subtree of G with n nodes, for some n≤N (the spanning tree case correspond to n=N, and is already deeply studied in the literature). We provide new asymptotically exact simulation methods using Markov chains for general connected graphs G, and any n≤N. We highlight the case of the uniform subtree of Z2 with n nodes, containing the origin (0,0) for which Schramm asked several questions. We produce pictures, statistics, and some conjectures. A second aim of the paper is devoted to surveying other models of random subtrees of a graph, among them, DLA models, the first passage percolation, the uniform spanning tree and the minimum spanning tree. We also provide new models, some statistics, and some conjectures.
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来源期刊
Probability Surveys
Probability Surveys STATISTICS & PROBABILITY-
CiteScore
4.70
自引率
0.00%
发文量
9
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