Related papers: Muttalib--Borodin ensembles in random matrix theor…
We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing…
An interesting first order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of attractive three-body interaction. We re-visit the…
We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ of dimensionality $mn$ in a Gaussian ensemble of random, complex pure states of the composite system. For a given dimensionality $m$ of the subsystem $A$,…
Consider the product of $M$ quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary…
$N$-dimensional Bessel and Jacobi processes describe interacting particle systems with $N$ particles and are related to $\beta$-Hermite, $\beta$-Laguerre, and $\beta$-Jacobi ensembles. For fixed $N$ there exist associated weak limit…
Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a…
The recently derived Fourier--Matsubara expansion of imaginary--time correlation functions comprises an exact result of linear response theory for finite-temperature quantum many-body systems. In its density--density version, the expansion…
We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues $\{\lambda_i\}$ of $N\times N$ Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these…
Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions…
The relativistic Hartree-Bogoliubov (RHB) model is extended to include density dependent meson-nucleon couplings. The effective Lagrangian is characterized by a phenomenological density dependence for the $\sigma$, $\omega$ and $\rho$…
Let $\mathbf{W}_1$ and $\mathbf{W}_2$ be independent $n\times n$ complex central Wishart matrices with $m_1$ and $m_2$ degrees of freedom respectively. This paper is concerned with the extreme eigenvalue distributions of double-Wishart…
We study the induced spherical ensemble of non-Hermitian matrices with real quaternion entries (considering each quaternion as a $2\times 2$ complex matrix). We define the ensemble by the matrix probability distribution function that is…
Duality identities in random matrix theory for products and powers of characteristic polynomials, and for moments, are reviewed. The structure of a typical duality identity for the average of a positive integer power $k$ of the…
We prove a compactness and integral-representation theorem for sequences of families of lattice energies describing atomistic interactions defined on lattices with vanishing lattice spacing. The densities of these energies may depend on…
We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation…
An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue…
We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings…
For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | \lambda_i - \lambda_j |^\beta \prod^n_{i=1} (2 - \lambda_i)^a (2 + \lambda_i)^b I_{(-2,2)} (\lambda_i) $$ $(a, b > -1, \beta > 0) $ a…
Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper deals with beta Jacobi ensembles, the type with the Jacobi…
The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric…