Related papers: The Gaussian Correlation Inequality for Symmetric …
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell…
A celebrated result by Gordon allows one to compare the min-max behavior of two Gaussian processes if certain inequality conditions are met. The consequences of this result include the Gaussian min-max (GMT) and convex Gaussian min-max…
Regarding the conjugacy representation on symmetric groups, we initiate a normalized measure emerging from this representation, namely the conjugacy measure. A central limit theorem for character ratios of random representations of the…
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…
Based on the notion of maximal correlation, Kimeldorf, May and Sampson (1980) introduce a measure of correlation between two random variables, called the "concordant monotone correlation" (CMC). We revisit, generalize and prove new…
We prove the 3-dimensional Gaussian product inequality, i.e., for any real-valued centered Gaussian random vector $(X,Y,Z)$ and $m\in \mathbb{N}$, it holds that…
We characterize the symmetric measures which satisfy the one dimensional convex Poincar\'e inequality. For these measures the tenesorization argument yields concentration inequalities for their products and convex sets in R^n.
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.
(Discriminative) Correlation Filter has been successfully applied to visual tracking and has advanced the field significantly in recent years. Correlation filter-based trackers consider visual tracking as a problem of matching the feature…
We discuss an analytic form of the dilation inequality for symmetric convex sets in Euclidean spaces, which is a counterpart of analytic aspects of Cheeger's isoperimetric inequality. We show that the dilation inequality for symmetric…
This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related…
This paper concerns a method of testing equality of distribution of random convex compact sets and the way how to use the test to distinguish between two realisations of general random sets. The family of metrics on the space of…
We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we…
We establish a general criterion for the validity of inequalities of the following form: A certain convex combination of the values of a convex function at n points and of its value at a weighted mean of these n points is always greater or…
We study the analogue of a convex interpolant of two sets on Sierpinski gaskets and an associated notion of measure transport. The structure of a natural family of interpolating measures is described and an interpolation inequality is…
This paper establishes quantitative correlation inequalities between monotone events and structured threshold objects in both the discrete cube and Gaussian space. We prove that for any increasing balanced family, there exists a linear…
This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions by Zhou et al. (2024), continues to hold for an arbitrary…
An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.