Related papers: Applications of Large Random Matrices in Communica…
The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
A striking prediction from the random matrix theory in mesoscopic physics is the existence of "open channels": waves that can use multipath interference to achieve perfect transmission across an opaque disordered medium even in the…
This paper is centred on the spectral study of a Random Fourier matrix, that is an $n\times n$ matrix $A$ whose $(j, k)$ entries are $\exp(2i\pi m X_jY_k)$, with $X_j$ and $Y_k$ two i.i.d sequences of random variables and $1\leq m\leq n$ is…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, $(Y_\ell)_{\ell =1}^n \in \mathbb{R}^d$, are i.i.d. draws of a…
Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…
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,…
In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. The limiting distribution is well described by its moments. Here, an analytical approach allows us, as in the case of Wigner…
Random media with tailored optical properties are attracting burgeoning interest for applications in imaging, biophysics, energy, nanomedicine, spectroscopy, cryptography and telecommunications. A key paradigm for devices based on this…
Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…