Theory of random matrices with strong level confinement: orthogonal polynomial approach

Details Theory of random matrices with strong level confinement: orthogonal polynomial approach Theory of random matrices with strong level confinement: orthogonal polynomial approach

1996-04-14

arxiv.org/abs/cond-mat/9604078v2

Physical Review E 54, 210 (1996)

Physics

Condensed Matter

12 pages (latex), to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.54.210

Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal with respect to exponential weights we calculate with asymptotic accuracy the two-point kernel over all distance scale, and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the endpoints of spectrum. We also obtain exact expressions for density of levels, one- and two-point Green's functions, and prove that new universal local relationship exists for suitably normalized and rescaled connected two-point Green's function. Connection between structure of Szeg\"o function entering strong polynomial asymptotics and mean-field equation is traced.

Affiliated with

Also associated with

No associations

Rating

Theory of random matrices with strong level confinement: orthogonal polynomial approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Theory of random matrices with strong level confinement: orthogonal polynomial approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Theory of random matrices with strong level confinement: orthogonal polynomial approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-526267