Related papers: Muttalib--Borodin ensembles in random matrix theor…
Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $\lambda$ describing logarithmic soft-confinement potentials $V(H) \sim [\ln H]^{(1+\lambda)} \:(\lambda>0$). We showed that…
We solve a family of Gaussian two-matrix models with rectangular Nx(N+v) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter mu. Our model can be thought of as the chiral extension of the real…
In the classical $\beta$-ensembles of random matrix theory, setting $\beta = 2 \alpha/N$ and taking the $N \to \infty$ limit gives a statistical state depending on $\alpha$. Using the loop equations for the classical $\beta$-ensembles, we…
We consider Hermite and Laguerre $\beta$-ensembles of large $N\times N$ random matrices. For all $\beta$ even, corrections to the limiting global density are obtained, and the limiting density at the soft edge is evaluated. We use the…
With $<\cdot>$ denoting an average with respect to the eigenvalue PDF for the Laguerre unitary ensemble, the object of our study is $ \tilde{E}_N(I;a,\mu) := < \prod_{l=1}^N \chi_{(0,\infty)\backslash I}^{(l)} (\lambda - \lambda_l)^\mu>$…
The $\beta$-ensembles of random matrix theory with classical weights have many special properties. One is that the loop equations specifying the resolvent and corresponding multipoint correlators permit a derivation at general order of the…
In this manuscript we study tridiagonal random matrix models related to the classical $\beta$-ensembles (Gaussian, Laguerre, Jacobi) in the high temperature regime, i.e. when the size $N$ of the matrix tends to infinity with the constraint…
The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire…
We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only…
We present finite-temperature, lattice Monte Carlo calculations of the particle number density, compressibility, pressure, and Tan's contact of an unpolarized system of short-range, attractively interacting spin-1/2 fermions in one spatial…
We construct and apply an exchange-correlation functional for the one-dimensional Hubbard model. This functional has built into it the Luttinger-liquid and Mott-insulator correlations, present in the Hubbard model, in the same way in which…
We propose a procedure to engineer solid-state lattice models with superlattices of interaction-coupled Bose-Einstein condensates. We show that the dynamical equation for the excitations of Bose-Einstein condensates at zero temperature can…
This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
We derive exact results for gap probabilities, as well as densities of extreme eigenvalues for six complex random matrix ensembles of fundamental importance. These are Gauss-Wigner, Laguerre-Wishart, Cauchy-Lorentz (two variants),…
Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…
Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…
Bourgade, Nikeghbali and Rouault recently proposed a matrix model for the circular Jacobi $\beta$-ensemble, which is a generalization of the Dyson circular $\beta$-ensemble but equipped with an additional parameter $b$, and further studied…
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin, $\textit{et al.}$, Nature $\textbf{609}$, 485 (2022)], we study a one-dimensional version of the two-component extended…