Related papers: Efron-Stein Inequalities for Random Matrices
This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
We prove that the classical Efron--Stein inequality holds for independent exchangeable pairs \((X_i,Y_i)\). The same inequality fails for independent identically distributed pairs; a simple trigonometric counterexample shows that the…
The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of…
Analyzing concentration of large random matrices is a common task in a wide variety of fields. Given independent random variables, many tools are available to analyze random matrices whose entries are linear in the variables, e.g. the…
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
The main purpose of this paper is to establish a noncommutative analogue of the Efron--Stein inequality, which bounds the variance of a general function of some independent random variables. Moreover, we state an operator version including…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
We propose a novel coupling inequality of the min-max type for two random matrices with finite absolute third moments, which generalizes the quantitative versions of the well-known inequalities by Gordon. Previous results have calculated…
We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…
We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of…
Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work…
In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix…
Matrix concentration inequalities provide information about the probability that a random matrix is close to its expectation with respect to the $l_2$ operator norm. This paper uses semigroup methods to derive sharp nonlinear matrix…
In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various…