相关论文: Where is Randomness Needed to Break the Square-Roo…
The groups $O(N)$ and $Sp(N)$ are related by an analytic continuation to negative values of $N$, $O(-N)\simeq Sp(N)$. This duality has been studied for vector models, $SO(N)$ and $Sp(N)$ gauge theories, as well as some random matrix…
Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus not explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where…
Spontaneous symmetry breaking (SSB) is the cornerstone of our understanding of quantum phases of matter. Recent works have generalized this concept to the domain of mixed states in open quantum systems, where symmetries can be realized in…
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…
Compressed sensing seeks to invert an underdetermined linear system by exploiting additional knowledge of the true solution. Over the last decade, several instances of compressed sensing have been studied for various applications, and for…
In the first five sections, we deal with the class of probability measures with asymptotically periodic Verblunsky coefficients of p-type bounded variation. The goal is to investigate the perturbation of the Verblunsky coefficients when we…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…
Working in high-dimensional latent spaces, the internal encoding of data in Variational Autoencoders becomes naturally sparse. We discuss this known but controversial phenomenon sometimes refereed to as overpruning, to emphasize the…
We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth…
Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…
Random subsampling of edges is a commonly employed technique in graph algorithms, underlying a vast array of modern algorithmic breakthroughs. Unfortunately, using this technique often leads to randomized algorithms with no clear path to…
The recent development of bootstrap methods based on semidefinite relaxations of positivity constraints has enabled rigorous two-sided bounds on local observables directly in the thermodynamic limit. However, these bounds inevitably become…
A long-standing sample compression conjecture asks to linearly bound the size of the optimal sample compression schemes by the Vapnik-Chervonenkis (VC) dimension of an arbitrary class. In this paper, we explore the rich metric and…
In this paper, we investigate the sample complexity of recovering tensors with low symmetric rank from symmetric rank-one measurements. This setting is particularly motivated by the study of higher-order interactions and the analysis of…
We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the…