相关论文: Concentration for matrix martingales in continuous…

In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for discrete-time matrix local martingales,…

In this work, Bernstein's concentration inequalities for squared integrable matrix-valued discrete-time martingales are obtained. Based on Lieb's theory and Bernstein's condition, a suitable supermartingale can be constructed. Our proof is…

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 give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…

This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…

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…

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…

We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing…

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of…

We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the ``intrinsic''…

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…

We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…

We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities…

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…

We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…

We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…

We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by…

The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matrices in terms of an associated noncommutative model. These…

The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…