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This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

This article introduces the operator-scaling random ball model, generalizing the isotropic random ball models investigated recently in the literature to anisotropic setup. The model is introduced as a generalized random field and results on…

One of the primary challenges of system identification is determining how much data is necessary to adequately fit a model. Non-asymptotic characterizations of the performance of system identification methods provide this knowledge. Such…

We introduce asymptotic analogues of the Rademacher and martingale type and cotype of Banach spaces and operators acting on them. Some classical local theory results related, for example, to the `automatic-type' phenomenon, the type-cotype…

We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A…

We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of…

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data…

In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the…

This paper investigates the estimation of radio channel parameters from receiver data, whereby the transmitter is fully unknown. We use a multipath model to describe the radio channel between transmitter and receiver. According to this…

A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We…

This paper considers a random access system where each sender can be in two modes of operation, active or not active, and where the set of active users is available to a common receiver only. Active transmitters encode data into independent…

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…

The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…

We apply an asymptotic bootstrap estimate method to the non-perturbative study of unitary matrix integrals. The method combines exact recursion relations with asymptotic control of large modes to achieve very high numerical precision…

A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…

We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…

We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…

In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…

This paper proposes methods for likelihood-based inference in multivariate linear regressions when the correlation matrix of the responses is separable; that is, it has a Kronecker product structure, but the variances are unrestricted. The…

Communication systems aided by movable antennas have been the subject of recent research due to their potentially increased spatial degrees of freedom offered by optimizing the antenna positioning at the transmitter and/or receiver. In this…