Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime
Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime
复制标题
热力学范围内贝蒂数的强大数定律
DOI：
10.1007/s10955-018-2201-z
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发表时间：
2018
影响因子：
1.6
通讯作者：
Tsunoda Kenkichi
中科院分区：
文献类型：
--
作者：
Goel Akshay;Trinh Khanh Duy;Tsunoda Kenkichi
在热力学体系中，我们建立了建立在二项点过程和相关Poisson点过程上的随机Čech复形的Betti数的强大数定律。在这里，我们考虑的情况下，潜在的点过程的分布是绝对连续的Lebesgue措施和情况下，它是支持紧流形的维数严格小于坦恩。在非常温和的假设下证明了强定律，该假设仅要求公共概率密度函数属于空间，对于所有的。
We establish the strong law of large numbers for Betti numbers of random Čech complexes built on-valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the case where the underlying distribution of the point processes is absolutely continuous with respect to the Lebesgue measure onand the case where it is supported on acompact manifold of dimension strictly less thanN. The strong law is proved under very mild assumption which only requires that the common probability density function belongs tospaces, for all.