Related papers: Random matrix statistics and zeroes of $L$-functio…
We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…
The statistics of low-lying zeros of quadratic Dirichlet L-functions were conjectured by Katz and Sarnak to be given by the scaling limit of eigenvalues from the unitary symplectic ensemble. The n-level densities were found to be in…
In this work, linearized multivariate skew polynomials over division rings are introduced. Such polynomials are right linear over the corresponding centralizer and generalize linearized polynomial rings over finite fields, group rings or…
It is shown that the correlation functions of the random variables $\det(\lambda - X)$, in which $X$ is a real symmetric $ N\times N$ random matrix, exhibit universal local statistics in the large $N$ limit. The derivation relies on an…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
We introduce a new type of convergence in probability theory, which we call ``mod-Gaussian convergence''. It is directly inspired by theorems and conjectures, in random matrix theory and number theory, concerning moments of values of…
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized on a random lattice…
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…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
Dixon's famous theorem states that the group generated by two random permutations of a finite set is generically either the whole symmetric group or the alternating group. In the context of random generation of finite groups this means that…
We propose a framework to study models of computation of indeterministic data, represented by abstract "distributions". In these distributions, probabilities are replaced by "amplitudes" drawn from a fixed semi-ring $S$, of which the…
Recently, an analytic method was developed to study in the large $N$ limit non-hermitean random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability distributions, thus extending the existing Gaussian…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
In Part I (G.Olshanski, math.RT/9804086) and Part II (A.Borodin, math.RT/9804087) we developed an approach to certain probability distributions on the Thoma simplex. The latter has infinite dimension and is a kind of dual object for the…
In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…