Related papers: Anti-concentration and the Exact Gap-Hamming Probl…

We consider two types of problems: maximising, over subsets $S\subseteq \{0,1\}^n$, the density of $d$-subcubes $C$ in the $n$-hypercube graph that span a subgraph such that $S\cap C$ is i) isomorphic to the given configuration…

We consider the problem of shared randomness-assisted multiple access channel (MAC) simulation for product inputs and characterize the one-shot communication cost region via almost-matching inner and outer bounds in terms of the smooth…

We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…

Motivated by the broadcast view of the interference channel, the new problem of communication with disturbance constraints is formulated. The rate-disturbance region is established for the single constraint case and the optimal encoding…

An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained…

The distribution of the properly renormalized gaps of $\sqrt{n} \,\mathrm{mod}\, 1$ with $n < N$ converges (when $N\rightarrow \infty$) to a non-standard limit distribution, as Elkies and McMullen proved in 2004 using techniques from…

We provide moment bounds for expressions of the type $(X^{(1)} \otimes \dots \otimes X^{(d)})^T A (X^{(1)} \otimes \dots \otimes X^{(d)})$ where $\otimes$ denotes the Kronecker product and $X^{(1)}, \dots, X^{(d)}$ are random vectors with…

Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued…

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of…

The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space $M$, we…

Let $G$ be a random group in Gromov's density model $G(m,d,L)$ with $d<\tfrac12$. We prove a sharp quantitative constraint on products of conjugates equal to the identity: for every $n\ge1$ and $\varepsilon>0$, with overwhelming probability…

We improve Knabe's spectral gap bound for frustration-free translation-invariant local Hamiltonians in 1D. The bound is based on a relationship between global and local gaps. The global gap is the spectral gap of a size-$m$ chain with…

The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…

We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…

We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required…

This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network whose cut-set bound is tight, i.e.,…

Let $\lambda_{max}$ be a shifted maximal real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix') in the $N\to\infty$ limit. It was shown by Poplavskyi, Tribe, Zaboronski \cite{PZT} that…

This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under a peak-power constraint. This work determines the largest peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution uniformly…

We show that, for many choices of finite tuples of generators $X = (x_1, \dots , x_d)$ of a tracial von Neumann algebra $(M, \tau)$ satisfying certain decomposition properties (non-primeness, possessing a Cartan subalgebra, or property…

Multi-channel wireless systems have become a standard solution to address our information society's ever-increasing demand for more information transfer. The ultimate bound on the capacity such systems can achieve is the limited channel…