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Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…

We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…

Sending quantum information reliably over long distances is a central challenge in quantum technology in general, and in quantum optics in particular, since most quantum communication relies on optical fibres or free-space links. Here, we…

This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…

In the study of the capacity problem for multiple access channels (MACs), a lower bound on the error probability obtained by Han plays a crucial role in the converse parts of several kinds of channel coding theorems in the…

In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the…

Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…

We study the convergence problem for mean field control, also known as optimal control of McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the limiting value function $\mathcal{U} :[0,T] \times…

We consider the problem of bounded-error quantum state identification: given either state \alpha_0 or state \alpha_1, we are required to output `0', `1' or `?' ("don't know"), such that conditioned on outputting `0' or `1', our guess is…

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 prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homogeneous weights. Inspired by the proof of such isoperimetric…

We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very small class of test boxes, which allows us to reduce…

In this article, we tackle the problem of the existence of a gap corresponding to Young measure relaxations for state-constrained optimal control problems. We provide a counterexample proving that a gap may occur in a very regular setting,…

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of…

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of…

We consider the task of distributed inner product estimation when allowed limited quantum communication. Here, Alice and Bob are given $k$ copies of an unknown $n$-qubit quantum states $\vert \psi \rangle,\vert \phi \rangle$ respectively.…

This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…

In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sa\u{g}lam and Tardos and Brody et al. showed…

This paper addresses two related problems in optimal control. The first investigation consists of compatibility issues between two classical approaches to deriving necessary conditions for optimal control problems with a final target: the…

This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…