Related papers: Contraction and decoupling inequalities for multil…
We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…
We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
We find the exact values for constants in bilateral Calderon-Stein-Weiss inequalities between tail (Marcinkiewicz) norm and weak Lebesgue (Lorentz) norm. Possible applications: Functional Analysis (for instance, interpolation of operators),…
We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
For each positive integer $d$, we prove a uniform $l^2$-decoupling inequality for the collection of all polynomials phases of degree at most $d$. Our result is intimately related to \cite{MR4078083}, but we use a different partition that is…
Let X_1, X_2,..., X_n be a sequence of independent random variables, let M be a rearrangement invariant space on the underlying probability space, and let N be a symmetric sequence space. This paper gives an approximate formula for the…
In recent years, it has been shown that some classical inequalities follow from a local stochastic dominance for naturally associated random polytopes. We strengthen planar isoperimetric inequalities by attaching a stochastic model to some…
The contraction inequality for Rademacher averages is extended to Lipschitz functions with vector-valued domains, and it is also shown that in the bounding expression the Rademacher variables can be replaced by arbitrary iid symmetric and…
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…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
A {\em maximal inequality} seeks to estimate $\mathbb{E}\max_i X_i$ in terms of properties of the $X_i$. When the latter are independent, the union bound (in its various guises) can yield tight upper bounds. If, however, the $X_i$ are…
Let (f_n) and (g_n) be two sequences of random variables adapted to an increasing sequence of $\sigma$-algebras $({\cal F}_n)$ such that the conditional distributions of f_n and g_n given ${\cal F}_{n-1}$ coincide, and such that the…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category,…
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
We prove several different anti-concentration inequalities for functions of independent Bernoulli-distributed random variables. First, motivated by a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn, we prove some "Poisson-type"…
We employ the combinatorial atlas technology to prove new correlation inequalities for the number of linear extensions of finite posets. These include the approximate independence of probabilities and expectations of values of random linear…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…