Corpus ID: 236976344

A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications

@inproceedings{Eichelsbacher2021ASS,
  title={A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications},
  author={Peter Eichelsbacher and Benedikt Rednoss and Christoph Thale and Guangqu Zheng},
  year={2021}
}
Abstract. In this paper, a simplified second-order Gaussian Poincaré inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, which is established by means of the discrete Malliavin-Stein method and is of independent interest. As an application, the number of vertices with prescribed degree and the subgraph counting… Expand

Figures from this paper

References

SHOWING 1-10 OF 42 REFERENCES
Multivariate central limit theorems for Rademacher functionals with applications
Quantitative multivariate central limit theorems for general functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences are proved by combining discrete MalliavinExpand
Normal approximation on Poisson spaces: Mehler’s formula, second order Poincaré inequalities and stabilization
We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure).Expand
Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation
A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein methodExpand
Fluctuations of eigenvalues and second order Poincaré inequalities
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hardExpand
Stein's method for normal approximation
Stein’s method originated in 1972 in a paper in the Proceedings of the Sixth Berkeley Symposium. In that paper, he introduced the method in order to determine the accuracy of the normal approximationExpand
Stein's Method and Stochastic Analysis of Rademacher Functionals
We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein's method, as well as the use of appropriate discrete MalliavinExpand
Berry-Esseen bounds for functionals of independent random variables
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weakExpand
Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals
In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables. In particular, we provide a newExpand
A non-uniform Berry–Esseen bound via Stein's method
Abstract. This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result is a proof for a non-uniform Berry–Esseen bound for independentExpand
A central limit theorem for decomposable random variables with applications to random graphs
TLDR
Stein's method of obtaining rates of convergence to the normal distribution is illustrated in the context of random graph theory and results are obtained for the number of copies of a given graph G in K. Expand
...
1
2
3
4
5
...