The Phase Transition in the Configuration Model
The Phase Transition in the Configuration Model
复制标题
配置模型中的相变
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
O. Riordan
中科院分区：
文献类型：
--
作者：
O. Riordan
设G = G（d）是一个具有给定度序列d的随机图，如一个随机r-正则图，其中r ≥ 3是固定的，n =| G| → ∞。我们研究了这类图G上的渗流相变，即，在随机子图G[p]中，当p增加时，通过以概率p保持边独立而获得的唯一巨分支的出现。更一般地，我们研究了当d变化时G（d）自身中巨分支的出现。我们表明，一个单一的方法可以用来证明非常精确的结果下面，里面和上面的“缩放窗口”的相变，匹配的许多已知的结果更简单的模型G（n，p）。这种方法是Bollobás和作者研究G（n，p）所用方法的自然延伸，G（n，p）本身是基于Aldous和Nacheland和Peres的工作;计算在目前的环境中明显更多地涉及。
Let G = G(d) be a random graph with a given degree sequence d, such as a random r-regular graph where r ≥ 3 is fixed and n = |G| → ∞. We study the percolation phase transition on such graphs G, i.e., the emergence as p increases of a unique giant component in the random subgraph G[p] obtained by keeping edges independently with probability p. More generally, we study the emergence of a giant component in G(d) itself as d varies. We show that a single method can be used to prove very precise results below, inside and above the ‘scaling window’ of the phase transition, matching many of the known results for the much simpler model G(n, p). This method is a natural extension of that used by Bollobás and the author to study G(n, p), itself based on work of Aldous and of Nachmias and Peres; the calculations are significantly more involved in the present setting.