Nonhermitean Random Matrix Models

Details Nonhermitean Random Matrix Models Nonhermitean Random Matrix Models

1996-12-29

arxiv.org/abs/cond-mat/9612240v2

Nucl.Phys. B501 (1997) 603-642

Physics

Condensed Matter

49 pages RevTex, with modified feynmf sty, 9 EPSF figures included. Version submitted to Nuclear Physics B

Scientific paper

10.1016/S0550-3213(97)00418-5

We introduce an extension of the diagrammatic rules in random matrix theory and apply it to nonhermitean random matrix models using the 1/N approximation. A number of one- and two-point functions are evaluated on their holomorphic and nonholomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic correlations. Generic form for the two-point functions are obtained, generalizing the concept of macroscopic universality to nonhermitean random matrices. We show that the holomorphic and nonholomorphic one- and two-point functions condition the behavior of pertinent partition functions to order $O(1/N)$. We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.

Affiliated with

Also associated with

No associations

Rating

Nonhermitean Random Matrix Models 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 Nonhermitean Random Matrix Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonhermitean Random Matrix Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-608719