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We describe an iterative scheme which allows us to calculate any multi-loopcorrelator for the complex matrix model to any genus using only the first inthe chain of loop equations. The method works for a completely generalpotential and the results contain no explicit reference to the couplings. Thegenus $g$ contribution to the $m$--loop correlator depends on a finite numberof parameters, namely at most $4g-2+m$. We find the generating functionalexplicitly up to genus three. We show as well that the model is equivalent toan external field problem for the complex matrix model with a logarithmicpotential.Comment: 17 page

HIGHER GENUS CORRELATORS FOR THE COMPLEX MATRIX MODEL