Related papers: Large deviations and stochastic calculus for large…
This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…
We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of Hermitian random matrices. We obtain new estimates related to the local semi-circular…
Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…
We experiment with some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We look at matrices defined by Gaussian primes and look at the growth of the…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. As an application we obtain a variational formula for the maximum of the support of a compactly supported…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices is formed by the adjacency matrix of an Erd\H{o}s-R\'{e}nyi graph $\mathcal{G}_{n,p}$ equipped with i.i.d.…
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…
In his seminal 1962 paper on the ``threefold way'', Freeman Dyson classified the spaces of matrices that support the random matrix ensembles deemed relevant from the point of view of classical quantum mechanics. Recently, Heinzner,…
The probability of the small deviations of the matrix $AA^T$ determinant is estimated, where $A$ is an $n\times\infty$ random matrix with centered entries having joint Gaussian distribution. The inequality obtained is sharp in a sence.
This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…