Random Kleinian Groups, II Two Parabolic Generators
Random Kleinian Groups, II Two Parabolic Generators
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DOI：
10.1080/10586458.2018.1477079
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发表时间：
2020-12-01
影响因子：
0.5
通讯作者：
Yamashita, Yasushi
中科院分区：
文献类型：
--
作者：
Martin, Gaven;O'Brien, Graeme;Yamashita, Yasushi
在早期的工作中，我们在所有莫比乌斯变换的群上引入了几何自然概率测度，以研究莫比乌斯变换的“随机”群、随机曲面，特别是随机两生成元群，即随机选择生成元的群，目的是估计这些群是离散的可能性，然后计算其相关参数的期望，几何学和拓扑学在本文中，我们继续研究和确定的精确概率，Fuchsian群产生的两个抛物Mobius变换是离散的，并给出估计的情况下，Kleinian群产生的一对随机抛物元素，我们支持与计算调查的Riley切片确定的Bowditch的条件，并建立严格的界限。
In earlier work, we introduced geometrically natural probability measures on the group of all Mobius transformations in order to study "random" groups of Mobius transformations, random surfaces, and in particular random two-generator groups, that is, groups where the generators are selected randomly, with a view to estimating the likelihood that such groups are discrete and then to make calculations of the expectation of their associated parameters, geometry, and topology. In this paper, we continue that study and identify the precise probability that a Fuchsian group generated by two parabolic Mobius transformations is discrete, and give estimates for the case of Kleinian groups generated by a pair of random parabolic elements which we support with a computational investigation of the Riley slice as identified by Bowditch's condition, and establish rigorous bounds.