The sub-Gaussian norm of a binary random variable

On the Spectral Norm of Gaussian Random Matrices

Let X be a d×d symmetric random matrix with independent but non-identically distributed Gaussian entries. It has been conjectured by Lata la that the spectral norm of X is always of the same order as the largest Euclidean norm of its rows. A positive resolution of this conjecture would provide a sharp understanding of the probabilistic mechanisms that control the spectral norm of inhomogeneous ...

Some applications of the Malliavin calculus to sub-Gaussian and non-sub-Gaussian random elds

We introduce a boundedness condition on the Malliavin derivative of a random variable to study subGaussian and other non-Gaussian properties of functionals of random …elds, with particular attention to the estimation of suprema. We relate the boundedness of nth Malliavin derivatives to a new class of “sub-nth Gaussian chaos” processes. An expected supremum estimation, extending the DudleyFerniq...

Autoregressive Gaussian Random Vectors of First Order

Chapter 1: Sub-Gaussian Random Variables

where μ = IE(X) ∈ IR and σ = var(X) > 0 are the mean and variance of X . We write X ∼ N (μ, σ). Note that X = σZ + μ for Z ∼ N (0, 1) (called standard Gaussian) and where the equality holds in distribution. Clearly, this distribution has unbounded support but it is well known that it has almost bounded support in the following sense: IP(|X −μ| ≤ 3σ) ≃ 0.997. This is due to the fast decay of the...

Matrix Decompositions Using sub-Gaussian Random Matrices

In recent years, several algorithms which approximate matrix decomposition have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We present a new algorithm, which achieves with high probability a rank-r SVD approximation of an n × n matrix and derive an error bound that does not depend on the first r singular values. Althou...