Related papers: A concentration inequality for product spaces

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 theory of multidimensional randomization in Lebesgue spaces $L^p$ with the aid of Kahane-Khintchine-Marcus-Pisier inequalities. More precisely, we obtain a result in the spirit of Maurey-Pisier's theorem which involves random…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\ldots, Z_m$, this article provides an expression of the concentration of functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each variable…

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…

Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…

We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…

Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…

We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic…

We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for…

We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…

In the paper we pursue the analysis from the section 5 of the Talagrand's paper "Sample boundedness of stochastic processes under increment conditions." Ann. Probab. 18, No. 1, 1-49. In particular we give the proof of some Sobolev…

Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…

We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test…

We prove Gaussian concentration inequalities for maximal displacement of compactly supported random walks on a compactly generated locally compact group with polynomial growth. Concentration inequalities with different exponents hold for…

We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.

Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.

This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…

Let $n\geq 1$, $K>0$, and let $X=(X_1,X_2,\dots,X_n)$ be a random vector in $\mathbb{R}^n$ with independent $K$--subgaussian components. We show that for every $1$--Lipschitz convex function $f$ in $\mathbb{R}^n$ (the Lipschitzness with…

In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…