Long range topological correlations in cellular patterns

In random 2D cellular assemblies, maximum entropy inference yields a specific form for the topological pair correlation, bi-affine in the cell charges (6-polygonality). By a self-consistent method, we show that the long distance behaviour of the pair correlation function is related to sum rules involving moments of the quadratic coefficients of the bi-affine form. The correlation function is predicted to decay like the 4th power of inverse distance if the first moment does not vanish, faster otherwise. The lowest sum rule expresses the screening of topological charge in the foam. Comparison with sparse available experimental data is not conclusive.