Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 87, 30 pp.
Multivariate central limit theorems for Rademacher functionals with applications
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.
Electron. J. Probab., Volume 22 (2017), paper no. 87, 30 pp.
Received: 25 January 2017
Accepted: 11 September 2017
First available in Project Euclid: 18 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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