相关论文: On invariant 2x2 \beta-ensembles of random matrice…

We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between theoretical predictions and empirical…

We introduce and study stochastic $N$-particle ensembles which are discretizations for general-$\beta$ log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, $(z,w)$-measures, etc. We…

We compute analytically the probability density function (pdf) of the largest eigenvalue $\lambda_{\max}$ in rotationally invariant Cauchy ensembles of $N\times N$ matrices. We consider unitary ($\beta = 2$), orthogonal ($\beta =1$) and…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…

We analyze a class of parametrized Random Matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function…

We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…

In this article, we consider $\beta$-ensembles, i.e. collections of particles with random positions on the real line having joint distribution $$\frac{1}{Z_N(\beta)}|\Delta(\lambda)|^\beta e^{- \frac{N\beta}{4}\sum_{i=1}^N\lambda_i^2}d…

We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS$_{3}$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random…

The general solution of the inverse Frobenius-Perron problem considering the construction of a fully chaotic dynamical system with given invariant density is obtained within the class of one-dimensional unimodal maps. Some interesting…

We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of…

Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes $\beta=1,2,4$. General formulas in terms of hyperdeterminants are found for…

We study a class of Hermitian random matrices which includes and generalizes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as the adjacency matrices of Erdos-Renyi random graphs with p ~ 1/N. Our NxN random…

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real $(\beta = 1)$, complex ($\beta = 2)$ and real…

We find the analytic expression of the trace of powers of the reduced density matrix on an interval of length L, for a massive boson field in 1+1 dimensions. This is given exactly (except for a non universal factor) in terms of a finite sum…

In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be…

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…

We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with…

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between…

We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special…