Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/460
Title: | Characteristic polynomials of complex random matrix models |
Authors: | Akemann, G Vernizzi, G |
Keywords: | High energy physics - theory;Mathematical physics |
Issue Date: | 2002 |
Publisher: | Elsevier Science |
Citation: | Nuclear Physics B660: 532-556, Dec 2002 |
Abstract: | We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of a determinant containing these polynomials and their kernel. It generalizes the known expression for hermitian matrices and it also provides a generalization of the Christoffel formula to the complex plane. The derivation we present holds for complex matrix models with a general weight function at finite-N, where N is the size of the matrix. We give some explicit examples at finite-N for specific weight functions. The characteristic polynomials in the large-N limit at weak and strong non-hermiticity follow easily and they are universal in the weak limit. We also comment on the issue of the BMN large-N limit. |
URI: | http://bura.brunel.ac.uk/handle/2438/460 |
DOI: | http://dx.doi.org/10.1016/S0550-3213(03)00221-9 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Characteristic Polynomials.pdf | 296.39 kB | Adobe PDF | View/Open |
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.