论文标题
密集的简单络合物的极限
Limits of Dense Simplicial Complexes
论文作者
论文摘要
我们开发了一个限制的理论，用于密集的抽象简单复合物的序列，如果其同态密度融合，则认为序列被认为会收敛。限制对象由可测量的[0,1]值的堆栈表示，在增加维度的单位立方体上，每个函数都对应于抽象简单复合物的维度。我们表明，同态密度的收敛意味着切割中的收敛，反之亦然，并且表明从极限对象采样的简单复合物与其结构非常相似。应用此框架，我们还部分表征了非均匀超图的收敛性。
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued functions on unit cubes of increasing dimension, each corresponding to a dimension of the abstract simplicial complex. We show that convergence in homomorphism density implies convergence in a cut-metric, and vice versa, as well as showing that simplicial complexes sampled from the limit objects closely resemble its structure. Applying this framework, we also partially characterize the convergence of nonuniform hypergraphs.
