Related papers: A concentration inequality for product spaces
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
In this work, we study pmp actions of countable groups on arbitrary diffuse probability spaces under the point of view of weak equivalence. We will show that any such an action is weakly equivalent to an action on a standard probability…
In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions…
We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are…
Self-normalized processes arise naturally in many learning-related tasks. While self-normalized concentration has been extensively studied for scalar-valued processes, there are few results for multidimensional processes outside of the…
Given a finite set $S$, i.i.d. random weights $\{X_i\}_{i\in S}$, and a family of subsets $\mathcal{F}\subseteq 2^S$, we consider the minimum weight of an $F\in \mathcal{F}$: \[ M(\mathcal{F}):= \min_{F\in \mathcal{F}} \sum_{i\in F}X_i. \]…
Concentration results say that a sequence of random variables becomes progressively concentrated around the mean. Such results are common in the study of functions of random graphs. We introduce a real-valued logic with various aggregate…
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of…
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 show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. Here we focus on differentiable functions on the Euclidean space in presence of a…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…
The purpose of these notes is to further complete our understanding of the stable concentration phenomenon, by obtaining the finite range behavior of $P(F-E[F]\geq x)$, with $F=f(X)$ where $f$ is a Lipschitz function and $X$ is a stable…
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…