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Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Given a rank-two sub-Riemannian structure $(M,\Delta)$ and a point $x_0\in M$, a singular curve is a critical point of the endpoint map $F:\gamma\mapsto\gamma(1)$ defined on the space of horizontal curves starting at $x_0$. The typical…

We prove that a connected graph has linear rank-width 1 if and only if it is a distance-hereditary graph and its split decomposition tree is a path. An immediate consequence is that one can decide in linear time whether a graph has linear…

This paper introduces the R package slm which stands for Stationary Linear Models. The package contains a set of statistical procedures for linear regression in the general context where the error process is strictly stationary with short…

Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…

We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If $X$ is the $n\times n$ symmetric matrix with $X_{ij}\sim N(0,b_{ij}^2)$, we show that…

Given a holomorphic iterated function scheme with a finite symmetry group $G$, we show that the associated dynamical zeta function factorizes into symmetry-reduced analytic zeta functions that are parametrized by the unitary irreducible…

We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invariant under translation by a full-rank sublattice L of Z^d; they…

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…

The low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This…

We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…

One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as…

We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are…

We study the dissipative spectral form factor (DSFF) at complex time $T e^{i\theta}$ for the complex elliptic Ginibre ensemble with non-Hermiticity parameter $\tau \in [0,1)$. As the matrix dimension $N \to \infty$, we consider the natural…

We give a linear-time algorithm that approximately uniformly generates a random simple graph with a power-law degree sequence whose exponent is at least 2.8811. While sampling graphs with power-law degree sequence of exponent at least 3 is…

Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…

We study the spectral norm of N-dimensional hermitian random matrices whose entries are zero outside of the band of the width b along the principal diagonal. Inside this band the elements are given by gaussian centered jointly independent…