Related papers: Decoupling inequalities with exponential constants
We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy…
Small ball inequalities have been extensively studied in the setting of Gaussian processes and associated Banach or Hilbert spaces. In this paper, we focus on studying small ball probabilities for sums or differences of independent,…
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer…
Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and…
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
Started from local universal isotropic disentanglement, a threshold inequality on reduction factors is proposed, which is necessary and sufficient for this type of disentanglement processes. Furthermore, we give the conditions realizing…
The generalized Bloch decomposition of a bipartite quantum state gives rise to a correlation matrix whose singular values provide rich information about non-local properties of the state, such as the dimensionality of entanglement. While…
We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detailed information about their geometry, and the percolative…
One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization.…
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…
In many realizations of beyond the Standard Model theories, new massive particles are introduced, leading to a multi-scale system with widely separated energy scales. In this setting the Coleman-Weinberg effective potential, which describes…
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
We propose a framework to analyze how multivariate representations disentangle ground-truth generative factors. A quantitative analysis of disentanglement has been based on metrics designed to compare how one variable explains each…
We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…
In previous work we established a multilinear duality and factorisation theory for norm inequalities for pointwise weighted geometric means of positive linear operators defined on normed lattices. In this paper we extend the reach of the…
Hexagon relations are algebraic realizations of four-dimensional Pachner moves. `Constant' -- not depending on a 4-simplex in a triangulation of a 4-manifold -- hexagon relations are proposed, and their polynomial-valued cohomology is…
We study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…