Multi-dimensional Gaussian fluctuations on the Poisson space

At the end of this chapter, we present an introduction to the three main original contributions in this dissertation: multi-dimensional CLTs on the Poisson space; Uni- versality

In particular, we shall provide a new analytic characterization of geometric random graphs whose edge-counting statistics exhibit asymptotic Gaussian fluctuations, and describe a

Several consequences are deduced from this result, in particu- lar: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed

present applications of the findings of [19] to the Gaussian fluctuation of statistics based on random graphs on a torus; reference [14] contains several multidimensional extensions

In particu- lar, we shall use our results in order to provide an exhaustive characterization of stationary geometric random graphs whose edge counting statistics exhibit

The purpose of this paper is to establish quantitative central limit theorems for some U -statistics on wavelets coef- ficients evaluated either on spherical Poisson fields or on

present applications of the findings of [19] to the Gaussian fluctuation of statistics based on random graphs on a torus; reference [14] contains several multidimensional extensions