相关论文: Correlation Functions of Complex Matrix Models

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…

We compute to all loop orders correlation function of four heavy BPS operators in $\mathcal{N}$= 4 SYM with special polarisations considered recently by Frank Coronado. Our main result is an expression for the octagon form factor as…

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.…

The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…

This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…

We consider the scaling Lee-Yang model. It corresponds to the unique perturbation of the minimal CFT model M(2,5). This is not a unitary model. We used known expression for form factors in order to obtain a closed expression for a…

The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system which we call the phase model is the strong…

We explain how the 't Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in N=4 super Yang-Mills theory. The full correlator in the limit is given by a non-trivial function of two variables: One…

We consider the quantum sinh-Gordon model in this paper. Using known formulae for form factors we sum up all their contributions and obtain a closed expression for a correlation function. This expression is a determinant of an integral…

We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a $N\times N$ random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding an…

We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system…

We consider correlation functions of topologically twisted, $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group ${\rm SU}(2)$ and $N_f\leq 3$ massive hypermultiplets in the fundamental representation. For a smooth, compact,…

In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional Gaussian complex matrix model. We develop a loop-equation based, analytic…

We compute the large scale (macroscopic) correlations in ensembles of normal random matrices with an arbitrary measure and in ensembles of general non-Hermition matrices with a class of non-Gaussian measures. In both cases the eigenvalues…

We study the structure of the normal matrix model (NMM). We show that all correlation functions of the model with axially symmetric potentials can be expressed in terms of holomorphic functions of one variable. This observation is used to…

Calculating the values of nuclear correlation functions is computationally intensive due to the fact that the number of terms in a nuclear wave function scales exponentially with atomic number. To speed up this computation, we represent a…

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…

We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…

We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…

We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature: we pursue the calculation and carry out the…