Random subgraph counts and u-statistics: Multivariate normal approximation via exchangeable pairs and embedding

Abstract

In Reinert and Röllin (2009) a new approach-called the 'embedding method'-was introduced, which allows us to make use of exchangeable pairs for normal and multivariate normal approximations with Stein's method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher-dimensional space in such a way that the linearity condition is then satisfied. Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs. © Applied Probability Trust 2010.