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Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering

   
@article{EJP2879,
	author = {Solesne Bourguin and Giovanni Peccati},
	title = {Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {Chen-Stein Method; Contractions; Malliavin Calculus; Poisson Limit Theorems; Poisson Space; Random Graphs; Total Variation Distance; Wiener Chaos},
	abstract = {Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of U-statistics following Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs.},
	pages = {no. 66, 1-42},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-2879},    
        url = {http://ejp.ejpecp.org/article/view/2879}}