Random groups arising as graph products
Random groups arising as graph products
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作为图产品出现的随机组
DOI：
10.2140/agt.2012.12.979
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发表时间：
2010
影响因子：
0.7
通讯作者：
M. Farber
中科院分区：
文献类型：
--
作者：
Ruth Charney;M. Farber
在本文中，我们研究了与随机图相关的图形产物产生的一类随机组的双曲性特性。回想一下，图产品的构造是对右角Artin和Coxeter组的结构的概括。我们采用随机图的ERDOS和RENYI模型，并为双曲线（或相对双曲线）找到精确的阈值函数。我们还研究了与随机图相关的右角ARTIN组的自动形态群体。我们表明，假设概率参数p是恒定的，并且满足0.2929 <p <1，则概率趋向于n-> n-> n->无穷大的ARTIN组具有有限的外部自身形态组。
In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled Artin and Coxeter groups. We adopt the Erdos and Renyi model of a random graph and find precise threshold functions for hyperbolicity (or relative hyperbolicity). We also study automorphism groups of right-angled Artin groups associated to random graphs. We show that with probability tending to one as n -> infinity, random right-angled Artin groups have finite outer automorphism groups, assuming that the probability parameter p is constant and satisfies 0.2929 < p < 1.