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

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
2.	Creator	Author's name, affiliation, country	Solesne Bourguin; University of Luxembourg; Luxembourg
2.	Creator	Author's name, affiliation, country	Giovanni Peccati; University of Luxembourg; Luxembourg
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Chen-Stein Method; Contractions; Malliavin Calculus; Poisson Limit Theorems; Poisson Space; Random Graphs; Total Variation Distance; Wiener Chaos
3.	Subject	Subject classification	60H07; 60F05; 60G55; 60D05
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-08-11
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2879
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2879
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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