Limit theory for point processes in manifolds
Limit theory for point processes in manifolds
Let $Y_i,i\geq1$, be i.i.d. random variables having values in an $m$-dimensional manifold $\mathcal {M}\subset \mathbb{R}^d$ and consider sums $\sum_{i=1}^nξ(n^{1/m}Y_i,\{n^{1/m}Y_j\}_{j=1}^n)$, where $ξ$ is a real valued function defined on pairs $(y,\mathcal {Y})$, with $y\in \mathbb{R}^d$ and $\mathcal {Y}\subset \mathbb{R}^d$ locally finite. Subject to $ξ$ satisfying a weak spatial dependence and continuity …