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This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
We study correlations of a set of stocks selected from both the New York and London stock exchanges. Results are displayed using both Random Matrix Theory approach and the graphical visualisation of the Minimal Spanning Tree. For the set of…
In this paper, we study cokernels of random $n\times n$ matrices over $\mathbb Z$ with symmetry conditions determined by fixed alternating bilinear forms on $\mathbb Z^n$. These include perturbations of random symmetric matrices at a very…
A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find $r$-dominating sets which enable…
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…
We study in this work the ground state entanglement properties of finite XX spin-1/2 chains with random couplings, using Jordan-Wigner transformation. We divide the system into two parts and study reduced density matrices (RDMs) of its…
It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average…
From the random matrix theory all the energy levels should be strongly correlated due to the presence of all off-diagonal entries.In this work we introduce two new statistics to more accurately characterize these long-distance interactions…
We prove the universal asymptotically almost sure non-singularity of general Ginibre and Wigner ensembles of random matrices when the distribution of the entries are independent but not necessarily identically distributed and may depend on…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
This paper presents an estimation method for time-varying graph signals among multiple sub-networks. In many sensor networks, signals observed are associated with nodes (i.e., sensors), and edges of the network represent the inter-node…
The Erd\H{o}s distance problem concerns the least number of distinct distances that can be determined by $N$ points in the plane. The integer lattice with $N$ points is known as \textit{near-optimal}, as it spans $\Theta(N/\sqrt{\log(N)})$…
In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of…