Related papers: Vector-valued concentration inequalities on the bi…
We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.
In this paper we survey known results of characterizations of reflexive Banach spaces, which are based on convergence of usual and generalized arithmetic mean (or Ces\`aro sum), weakly compact subsets, affine sets in a Banach space or its…
We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of $c_0$ and superreflexivity are discussed.
We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…
We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
This paper connects nonpositive sectional curvature of a Riemannian manifold with the displacement convexity of the variance functional on the space $P(M)$ of probability measures over $M$. We show that $M$ has nonpositive sectional…
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…
Understand and predict the dynamics of dispersed micro-objects in microfluidics is crucial in numerous natural, industrial and technological situations. In this paper, we experimentally characterized the equilibrium velocity $V$ and lateral…
Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we…
We are interested in Sobolev type inequalities and their relationship with concentration properties on higher dimensions. We consider unbounded spin systems on the d-dimensional lattice with interactions that increase slower than a…
Large-scale nonconvex and nonsmooth problems have attracted considerable attention in the fields of compress sensing, big data optimization and machine learning. Exploring effective methods is still the main challenge of today's research.…
We discuss a natural extension of Gilles Pisier's approach to the study of measure concentration, isoperimetry and Poincar\'e-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measure in…
Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace…
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 uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets,…
We prove large and moderate deviation results for sequences of compound sums, where the summands are i.i.d. random variables taking values in a separable Banach space. We establish that the results hold by proving that we are dealing with…
We collect several open questions in Banach spaces, mostly related to measure theoretic aspects of the theory. The problems are divided into five categories: miscellaneous problems in Banach spaces (non-separable $L^p$ spaces, compactness…