Related papers: Exact 2-point function in Hermitian matrix model
Brezin-Hikami contour-integral representation of exponential multidensities in finite N Hermitian matrix model is a remarkable implication of the old Hermitian-Kontsevich duality. It is also a simplified version of Okounkov's formulas for…
We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential…
Analytical expressions of some of the spin-spin correlation functions up to eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at zero temperature without magnetic field are obtained. The key object of our method is…
Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support…
We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with…
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
We present the $W_{1+\infty}$ constraints for the Gaussian Hermitian matrix model, where the constructed constraint operators yield the $W_{1+\infty}$ $n$-algebra. For the Virasoro constraints, we note that the constraint operators give the…
The k-point correlation functions of the Gaussian Random Matrix Ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We…
We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the…
The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…
The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance…
Using large $N$ arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large $N$ limit. The setting generalizes the quaternionic extension of free probability to…
We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…
In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which…
We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…
We derive the analogues of the Harer-Zagier formulas for single- and double-trace correlators in the q-deformed Hermitian Gaussian matrix model. This fully describes single-trace correlators and opens a road to $q$-deformations of important…
We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for $\beta^2=8\pi$, they reproduce the exactly known corresponding functions of the massless theory,…
We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at…