Related papers: Dual Loomis-Whitney inequalities via information t…
We consider two well-known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume of ellipsoids containing projections of convex bodies given…
Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated…
We introduce a new class of (not necessarily convex) bodies and show, among other things, that these bodies provide yet another link between convex geometric analysis and information theory. Namely, they give geometric interpretations of…
We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
The random polytope $K_n$, defined as the convex hull of $n$ points chosen uniformly at random on the boundary of a smooth convex body, is considered. Proofs for lower and upper variance bounds, strong laws of large numbers and central…
This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
Relative to the Gaussian measure on $\mathbb{R}^d$, entropy and Fisher information are famously related via Gross' logarithmic Sobolev inequality (LSI). These same functionals also separately satisfy convolution inequalities, as proved by…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex core. The first set of questions is to what extent the…
We introduce a refinement to the convex split lemma by replacing the max mutual information with the collision mutual information, transforming the inequality into an equality. This refinement yields tighter achievability bounds for quantum…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In the paper "Isoperimetry of waists and local versus global asymptotic convex geometries", it was proved that the existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of randomly rotated…
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr.~on the reverse question: Every convex body has a linear image whose…
We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…
We generalize the information lattice, originally defined for one-dimensional open-boundary chains, to characterize quantum many-body states in higher-dimensional geometries. In one dimension, the information lattice provides a position-…
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex…
Van Trees inequality, also known as the Bayesian Cram\'er-Rao lower bound, is a powerful tool for establishing lower bounds for minimax estimation through Fisher information. It easily adapts to different statistical models and often yields…
We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and…