Related papers: Towards mixed phase correlators in monomial matrix…

Macroscopic loop correlators are investigated in the hermitian one matrix model with the potential perturbed by the higher order curvature term. In the phase of smooth surfaces the model is equivalent to the minimal conformal matter coupled…

We argue that the recently discovered bilinear superintegrability arXiv:2206.02045 generalizes, in a non-trivial way, to monomial matrix models in pure phase. The structure is much richer: for the trivial core Schur functions required…

We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the…

We study $k$-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the real, complex and quaternion $N \times N$ Ginibre ensembles. Our approach is based on the technique of character…

We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.

We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This…

We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully…

We argue that restricted Schur polynomials provide a useful parameterization of the complete set of gauge invariant variables of multi-matrix models. The two point functions of restricted Schur polynomials are evaluated exactly in the free…

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of…

Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequently used and studied. These forms are upper-triangular…

Some puzzles which arise in matrix models with multiple cuts are presented. They are present in the smoothed eigenvalue correlators of these models. First a method is described to calculate smoothed eigenvalue correlators in random matrix…

We develop a new framework to compute the exact correlators of characteristic polynomials, and their inverses, in random matrix theory. Our results hold for general potentials and incorporate the effects of an external source. In matrix…

We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product…

A system of two self and mutual interacting ring polymers, close together in space, can display several competing equilibrium phases and phase transitions. Using Monte Carlo simulations and combinatorial arguments on a corresponding lattice…

Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using…

Some eigenvalue matrix models possess an interesting property: one can manifestly define the basis where all averages can be explicitly calculated. For example, in the Gaussian Hermitian and rectangular complex models, averages of the Schur…

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…

Many eigenvalue matrix models possess a peculiar basis of observables which have explicitly calculable averages. This explicit calculability is a stronger feature than ordinary integrability, just like the cases of quadratic and Coulomb…

Unitary 1-matrix models are shown to be exactly equivalent to hermitian 1-matrix models coupled to 2N vectors with appropriate potentials, to all orders in the 1/N expansion. This fact allows us to use all the techniques developed and…

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…