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We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
Asteroseismic large frequency separations possess great diagnostic value. However, their expressions as scaling relations are predicated on homology arguments which may not hold in general, resulting in mass- and temperature-dependent…
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…
Complex eigenvalues of random matrices $J=\text{GUE }+ i\gamma \diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
The extremal dependence structure of a regularly varying $d$-dimensional random vector can be described by its angular measure. The standard nonparametric estimator of this measure is the empirical measure of the observed angles of the $k$…
The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…
Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we…
In high-dimensional data, structured noise caused by observed and unobserved factors affecting multiple target variables simultaneously, imposes a serious challenge for modeling, by masking the often weak signal. Therefore, (1) explaining…
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…
Consider a standard white Wishart matrix with parameters $n$ and $p$. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the $m…
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint…
We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, where singular values below a prescribed threshold $\lambda$ are set to 0. We study the asymptotic MSE in a framework where the matrix size…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
A recent development in random matrix theory, the intrinsic freeness principle, establishes that the spectrum of very general random matrices behaves as that of an associated free operator. This reduces the study of such random matrices to…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
In the paper we study the discrete spectrum of a pair of quantum two-dimensional waveguides having common boundary in which a window of finite length is cut out. We study the phenomenon of new eigenvalues emerging from the threshold of the…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral…
This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The…