Related papers: Eigenvalue Attraction
This paper studies the action dynamics of network coordination games with bounded-rational agents. I apply the experience-weighted attraction (EWA) model to the analysis as the EWA model has several free parameters that can capture…
We analyse the numbers of closed paths of length $k\in\mathbb{N}$ on two important regular lattices: the hexagonal lattice (also called $\textit{graphene}$ in chemistry) and its dual triangular lattice. These numbers form a moment sequence…
Symmetrizable matrices are those which are symmetric when multiplied by a diagonal matrix with positive entries. The Cauchy interlace theorem states that the eigenvalues of a real symmetric matrix interlace with those of any principal…
Adsorption at an attractive surface in a system with particles self-assembling into small clusters is studied by Molecular dynamics (MD) simulation. We assume Lennard-Jones plus repulsive Yukawa tail interactions, and focus on small…
We investigate the evolution of a given eigenvector of a symmetric (deterministic or random) matrix under the addition of a matrix in the Gaussian orthogonal ensemble. We quantify the overlap between this single vector with the eigenvectors…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
Previous theoretical, along with early simulation and experimental, studies have indicated that particles with a short-ranged attraction exhibit a range of new dynamical arrest phenomena. These include very pronounced reentrance in the…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
We analyse the largest eigenvalue of the adjacency matrix of the configuration model with large degrees, where the latter are treated as hard constraints. In particular, we compute the expectation of the largest eigenvalue for degrees that…
The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction. However, the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments, which has…
This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the…
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…
We investigate self-adjoint matrices $A\in\mathbb{R}^{n,n}$ with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group…
Real vector fields $\dot{z} = f(z)$ in $\mathbb{R}^N$ extend to $\mathbb{C}^N$, for complex entire $f$. One known consequence are exponentially small upper bounds \begin{equation*} \label{*} C_\eta \exp(-\eta/\varepsilon) \tag{*}…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…
The statistical behaviour of the smallest eigenvalue has important implications for systems which can be modeled using a Wishart-Laguerre ensemble, the regular one or the fixed trace one. For example, the density of the smallest eigenvalue…
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…