Universal Gaussian fluctuations on the discrete Poisson chaos

Keywords: Central Limit Theorems; Malliavin calculus; Multi-dimensional normal ap- proximations; Ornstein-Uhlenbeck processes; Poisson measures; Probabilistic Interpola- tions;

Key words: Free Probability; Free Poisson Algebra; Multiple Wigner Integrals; Multiplica- tion Formula; Diagram Formula; Non–Crossing Partitions; Free Cumulants; Fourth Moment

We observe the number N of deaths within a window of time W (say T plus two weeks), and we assume that if an individual who has been infected in the window of time T dies, the death

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

Key words: Central Limit Theorems; Malliavin calculus; Multi-dimensional normal approxi- mations; Ornstein-Uhlenbeck processes; Poisson measures; Probabilistic Interpolations;

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

We find this part of his paper is very hard to read, and the purpose of our work is to use Talagrand’s generic chaining instead, this simplifies significantly Lata la’s proof..