Central Limit Theorem; On-line Nearest Neighbour Graph; Poisson Measure
Abstract :
[en] We establish new explicit bounds on the Gaussian approximation of Poisson functionals based
on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin-Stein
method, we derive bounds in the Wasserstein and Kolmogorov distances whose application requires
minimal moment assumptions on add-one cost operators – thereby extending the results from (Last,
Peccati and Schulte, 2016). Our applications include a CLT for the Online Nearest Neighbour
graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also apply
our techniques to derive quantitative CLTs for edge functionals of the Gilbert graph, of the k-Nearest Neighbour graph and of the Radial Spanning Tree, both in cases where qualitative CLTs
are known and unknown.
Disciplines :
Mathematics
Author, co-author :
TRAUTHWEIN, Tara ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
no
Language :
English
Title :
Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities
