Quantitative CLTs for Poisson Functionals with Applications to Random Graphs
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
Please Login in order to download this file