Factorisations for Partition Functions of Random Hermitian Matrix Models
نویسندگان
چکیده
Factorisations of partition functions of random Hermitian matrix models 1 2 Abstract The partition function ZN ; for Hermitian-complex matrix models can be expressed as an explicit integral over R N ; where N is a positive integer. Such an integral also occurs in connexion with random surfaces and models of two dimensional quantum gravity. We show that ZN can be expressed as the product of two partition functions, evaluated at translated arguments, for another model, giving an explicit connexion between the two models. We also give an alternative computation of the partition function for the 4-model. The approach is an algebraic one and holds for the functions regarded as formal power series in the appropriate ring.
منابع مشابه
New Developments in Non-hermitian Random Matrix Models
Random matrix models provide an interesting framework for modeling a number of physical phenomena, with applications ranging from atomic physics to quantum gravity 1, . In recent years, non-hermitian random matrix models have become increasingly important in a number of quantum problems 3, . A variety of methods have been devised to calculate with random matrix models. Most prominent perhaps ar...
متن کاملDynamical Correlations for Circular Ensembles of Random Matrices
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number ...
متن کاملAn iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...
متن کاملBoundary states, matrix factorisations and correlation functions for the E-models
The open string spectra of the B-type D-branes of the N = 2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E6 using conformal field theory methods, thereby enabling us to test results recently obtai...
متن کاملComputing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method
A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...
متن کامل