论文标题
马尔可夫空间中的子图密度
Subgraph densities in Markov spaces
论文作者
论文摘要
我们将在密集的图极限理论中产生的子图密度概括为马尔可夫空间（标准borel空间平方的对称度量）。更普遍地，我们以有限图的地图上的度量形式定义了一组同态的类似物。这种同态措施的存在并不总是可以保证，但是可以在马尔可夫空间上的自然平稳条件下建立，并在图表上建立稀疏条件。这延续了图表限制理论的方向，其中这种度量被视为图序列的限制。
We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure on maps of a finite graph into a Markov space. The existence of such homomorphism measures is not always guaranteed, but can be established under rather natural smoothness conditions on the Markov space and sparseness conditions on the graph. This continues a direction in graph limit theory in which such measures are viewed as limits of graph sequences.
