Electronic Journal of Probability

Multivariate central limit theorems for Rademacher functionals with applications

Kai Krokowski and Christoph Thäle

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 87, 30 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1508292258

Digital Object Identifier
doi:10.1214/17-EJP106

Mathematical Reviews number (MathSciNet)
MR3718714

Zentralblatt MATH identifier
06797897

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 05C80: Random graphs [See also 60B20] 60C05: Combinatorial probability 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60H07: Stochastic calculus of variations and the Malliavin calculus

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Krokowski, Kai; Thäle, Christoph. Multivariate central limit theorems for Rademacher functionals with applications. Electron. J. Probab. 22 (2017), paper no. 87, 30 pp. doi:10.1214/17-EJP106. https://projecteuclid.org/euclid.ejp/1508292258


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References

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