Poisson limits for U-statistics

We study Poisson limits for U-statistics with non-negative kernels. The limit theory is derived from the Poisson convergence of suitable point processes of U-statistics structure. We apply these results to derive infinite variance stable limits for U-statistics with a regularly varying kernel and to determine the index of regular variation of the left tail of the kernel. The latter is known as correlation dimension. We use the point process convergence to study the asymptotic behavior of some standard estimators of this dimension.