Universality of correlation functions of hermitian random matrices in an external field
نویسنده
چکیده
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 behavior is found to be identical to the one obtained in previously studied matrix models, thus extending the universality of the levelspacing distribution. The calculation of correlation functions involves (finite N) determinant formulae, reducing the problem to the large N asymptotic analysis of a single kernel K. This is performed by an appropriate matrix integral formulation of K. Multi-matrix generalizations of these results are discussed. ⋆ unité propre du CNRS, associée à l’Ecole Normale Supérieure et l’Université Paris-Sud.
منابع مشابه
Universality at the Edge of the Spectrum in Wigner Random Matrices
We prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit n → +∞. As a corollary, we show that, after proper rescaling, the 1st, 2nd, 3rd, etc. eigenvalues of Wigner random hermitian (or real symmetric) matrix weakly converge to the distributions established by Tracy and Widom in G.U.E. (G.O.E.) cases.
متن کاملRandom hermitian matrices in an external field
In this article, a model of random hermitian matrices is considered, in which the measure exp(−S) contains a general U(N)-invariant potential and an external source term: S = N tr(V (M) + MA). The generalization of known determinant formulae leads to compact expressions for the correlation functions of the energy levels. These expressions, exact at finite N , are potentially useful for asymptot...
متن کاملCorrelation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix
Abstract: The universality of correlation functions of eigenvalues of large random matrices has been observed in various physical systems, and proved in some particular cases, as the hermitian one-matrix model with polynomial potential. Here, we consider the more difficult case of a unidimensional chain of matrices with first neighbour couplings and polynomial potentials. An asymptotic expressi...
متن کاملEigenvalue Distribution In The Self-Dual Non-Hermitian Ensemble
We consider an ensemble of self-dual matrices with arbitrary complex entries. This ensemble is closely related to a previously defined ensemble of antisymmetric matrices with arbitrary complex entries. We study the two-level correlation functions numerically. Although no evidence of non-monotonicity is found in the real space correlation function, a definite shoulder is found. On the analytical...
متن کاملCorrelation Functions of Ensembles of Asymmetric Real Matrices
We give a closed form for the correlation functions of ensembles of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2×2 matrix kernel associated to the ensemble. We also derive closed forms for the matrix kernel and correlation functions for Ginibre’s real ensemble. Difficulties arise in the study of ensembles of asymmetric random matrices which do not...
متن کامل