论文标题
多参数简单复合物中子复合数和贝蒂数字的大偏差
Large deviations for subcomplex counts and Betti numbers in multi-parameter simplicial complexes
论文作者
论文摘要
我们将多参数随机简单复合物视为经典Erdös-Rényi图的较高维度扩展。我们从大偏差的角度研究了复合物中“异常”拓扑结构的外观。我们首先研究了子复合计数的上尾大偏差概率，以对数尺度的精度得出了此类概率的数量级。然后将获得的结果应用于分析临界维度及以下简单数量的大偏差。最后，这些结果还用于推断临界维度中复合物的贝蒂数量的大偏差估计值。
We consider the multi-parameter random simplicial complex as a higher dimensional extension of the classical Erdös-Rényi graph. We investigate appearance of "unusual" topological structures in the complex from the point of view of large deviations. We first study upper tail large deviation probabilities for subcomplex counts, deriving the order of magnitude of such probabilities at the logarithmic scale precision. The obtained results are then applied to analyze large deviations for the number of simplices at the critical dimension and below. Finally, these results are also used to deduce large deviation estimates for Betti numbers of the complex in the critical dimension.
