Related papers: Large Random Matrices: Eigenvalue Distribution
We prove universality for the fluctuations of the halting time for the Toda algorithm to compute the largest eigenvalue of real symmetric and complex Hermitian matrices. The proof relies on recent results on the statistics of the…
In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of large size perturbed by a random matrix with small operator norm whose entries in the…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
The remarkable universality of the eigenvalue correlation functions is perhaps one of the most salient findings in random matrix theory. Particularly for short-range separations of the eigenvalues, the correlation functions have been shown…
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
We solve the loop equations of the hermitian 2-matrix model to all orders in the topological $1/N^2$ expansion, i.e. we obtain all non-mixed correlation functions, in terms of residues on an algebraic curve. We give two representations of…
We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…
We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…
In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context…
We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…
In this paper, we first study the projections onto the set of unit dual quaternions, and the set of dual quaternion vectors with unit norms. Then we propose a power method for computing the dominant eigenvalue of a dual quaternion Hermitian…
We consider an ensemble of self-dual matrices with arbitrary complex entries. This ensemble is closely related to a previously defined ensemble of anti-symmetric matrices with arbitrary complex entries. We study the two-level correlation…
The $\tau$-function theory of Painlev\'e systems is used to derive recurrences in the rank $n$ of certain random matrix averages over U(n). These recurrences involve auxilary quantities which satisfy discrete Painlev\'e equations. The…
We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non--trivial saddle points, which break replica symmetry, must be included in the calculation in order…
This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…