Related papers: Revisiting Concentration of Missing Mass
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 some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
In this paper, we study the concentration properties of quadratic forms associated with Markov chains using the martingale decomposition method introduced by Atchad\'e and Cattaneo (2014). In particular, we derive concentration inequalities…
This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector $X \in \mathbb{R}^n$ with independent subgaussian components. The core technique of the paper is based on the entropy method combined with…
Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…
Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…
We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a…
We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's…
We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…
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 resonant absorption of light by an ensemble of absorbers decreases when the resonance is inhomogeneously broadened, as only a fraction of the ensemble contributes to the absorption at any given optical frequency. Recovering the lost…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functions on the unit sphere. Technically, our results are based on…
We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…
We show how to estimate a broad class of multipartite entanglement measures from Bell basis measurement data. In addition to lowering the experimental requirements relative to previously known methods of estimating these measures, our…
In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting as in Bouchitt\'e, Bourel and Felbacq (C.R. Math. Acad.…
We first investigate concentration and vanishing phenomena concerning Moser type inequalities in the whole plane which involve complete and reduced Sobolev norms. In particular we show that the critical Ruf inequality is equivalent to an…
Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\Gamma\backslash G$, where $G$ is any connected…
The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is…
We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean…