Mixed correlation functions of the two matrix model

Bertola, M.; Eynard, B.

doi:10.1088/0305-4470/36/28/304

Mixed correlation functions of the two matrix model

M. Bertola
(
- Concordia U., Math. Dept. and
- Montreal U., CRM
)
,
B. Eynard
(
- Montreal U., CRM and
- Saclay
)

Mar, 2003

16 pages

Published in:

J.Phys.A 36 (2003) 7733-7750

e-Print:

hep-th/0303161 [hep-th]

DOI:

10.1088/0305-4470/36/28/304

Report number:

CRM-2916,
SACLAY-T03-028

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Abstract:

We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature: we pursue the calculation and carry out the eigenvalue integration reducing the problem to the construction of the associated biorthogonal polynomials. The generating function of these correlations becomes then a determinant involving the recursion coefficients of the biorthogonal polynomials.

Note:

16 pages Report-no: CRM-2961, Saclay T03-028

matrix model: random
correlation function
symmetry: U(N)
perturbation theory: higher-order

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