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Quantifying convergence and sufficient sampling of macromolecular molecular dynamics simulations is more often than not a source of controversy (and of various ad hoc solutions) in the field. Clearly, the only reasonable, consistent and…
We study random matrices with independent subgaussian columns. Assuming each column has a fixed Euclidean norm, we establish conditions under which such matrices act as near-isometries when restricted to a given subset of their domain. We…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We show that real second order freeness appears in the study of Haar unitary and unitarily invariant random matrices when transposes are also considered. In particular we obtain the unexpected result that a unitarily invariant random matrix…
In this paper we study random matrix models where the matrices in question contain infinitely many spikes. Recent work has characterized the possible outliers in the spectrum of large deformed unitarily invariant models when the number of…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the…
Several sequences of free cumulants that count binary plane trees correspond to sequences of classical cumulants that count the decreasing versions of the same trees. Using two new operations on colored binary plane trees that we call…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…
We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
In this note we study asymptotic properties of the *-distribution of traces of some matrices, with respect to the free Haar trace on the unitary dual group. The considered matrices are powers of the unitary matrix generating the Brown…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
The asymptotic freeness of independent unitarily invariant $N\times N$ random matrices holds in expectation up to $O(N^{-2})$. An already known consequence is the infinitesimal freeness in expectation. We put in evidence another consequence…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
We apply the operation of random independent thinning on the eigenvalues of $n\times n$ Haar distributed unitary random matrices. We study gap probabilities for the thinned eigenvalues, and we study the statistics of the eigenvalues of…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…