Quantitative CLTs for Poisson Functionals with Applications to Random Graphs

Trauthwein Tara, University of Oxford

In this talk, we present new explicit bounds on the Gaussian approximation of Poisson functionals based on novel p-Poincaré inequalities. 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.

Area: CS41 - Limit theorems for random structures (Nicola Turchi)

Keywords: Quantitative CLTs; Random Graphs; Malliavin-Stein Method

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