Open Access
2017 Multivariate central limit theorems for Rademacher functionals with applications
Kai Krokowski, Christoph Thäle
Electron. J. Probab. 22: 1-30 (2017). DOI: 10.1214/17-EJP106


Quantitative multivariate central limit theorems for general functionals of independent, possibly non-symmetric and non-homogeneous infinite Rademacher sequences are proved by combining discrete Malliavin calculus with the smart path method for normal approximation. In particular, a discrete multivariate second-order Poincaré inequality is developed. As a first application, the normal approximation of vectors of subgraph counting statistics in the Erdős-Rényi random graph is considered. In this context, we further specialize to the normal approximation of vectors of vertex degrees. In a second application we prove a quantitative multivariate central limit theorem for vectors of intrinsic volumes induced by random cubical complexes.


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Kai Krokowski. Christoph Thäle. "Multivariate central limit theorems for Rademacher functionals with applications." Electron. J. Probab. 22 1 - 30, 2017.


Received: 25 January 2017; Accepted: 11 September 2017; Published: 2017
First available in Project Euclid: 18 October 2017

zbMATH: 06797897
MathSciNet: MR3718714
Digital Object Identifier: 10.1214/17-EJP106

Primary: 60F05
Secondary: 05C80 , 60C05 , 60D05 , 60H07

Keywords: Discrete Malliavin calculus , intrinsic volume , multivariate central limit theorem , random cubical complex , random graph , smart path method , subgraph count , vertex degree

Vol.22 • 2017
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