Limit Correlation Functions for Fixed Trace Random Matrix Ensembles
نویسندگان
چکیده
منابع مشابه
Limit Correlation Functions for Fixed Trace Random Matrix Ensembles
LetHN be the set of all N×N (complex) Hermitian matrices, and let trA = ∑N i=1 aii denotes the trace of a square matrix A = (aij) N i,j=1. HN is a real Hilbert space of dimension N with respect to the symmetric bilinear form (A,B) 7→ trAB. Let lN denotes the unique Lebesgue measure on HN which satisfies the relation lN(Q) = 1 for every cube Q ⊂ HN with edges of length 1. A Gaussian probability ...
متن کاملPfaffian Expressions for Random Matrix Correlation Functions
It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of Pfaffians. In this article, we review the formulations and applications of Pfaffian formulas. For that purpose, we first present the general Pfaffian e...
متن کاملTwo-level correlation function of critical random-matrix ensembles
The two-level correlation function Rd,β(s) of d-dimensional disordered models (d = 1, 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal (β = 1) or unitary (β = 2) symmetry in the strong (b ≪ 1) coupling regime, where the parameter b plays the role of the coupling constant of the model. It is found that Rd,β(s) is o...
متن کاملq-RANDOM MATRIX ENSEMBLES
With a few notable exceptions, the interaction between the community of mathematicians who work in special functions, in particular, those that are in the area of q-series and basic Hypergeometric functions and the physics community has so far been minimal. In this review article, we will describe some developments in one area in physics, namely the Theory of Random Matrix Ensembles, where a q-...
متن کاملNew Multicritical Random Matrix Ensembles
In this paper we construct a class of random matrix ensembles labelled by a real parameter α ∈ (0, 1), whose eigenvalue density near zero behaves like |x|α. The eigenvalue spacing near zero scales like 1/N1/(1+α) and thus these ensembles are representatives of a continous series of new universality classes. We study these ensembles both in the bulk and on the scale of eigenvalue spacing. In the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2008
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-008-0484-7