Topological correlations and asymptotic freedom in cellular aggregates

TL;DR

This paper investigates the topological pair correlations in random cellular systems, revealing their bi-affine form and conditions for statistical independence at large distances, with implications for layer population and topological charge growth.

Contribution

It explicitly derives the form of topological correlations and conditions for asymptotic independence in cellular aggregates, linking maximum entropy coefficients to large-distance behavior.

Findings

Topological pair correlation is bi-affine in cell edges.

Statistical independence occurs at large distances under certain conditions.

Layer population and topological charge grow polynomially with distance.

Abstract

In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two cells of the pair. Assuming this form for the pair correlations, we make explicit the conditions of statistical independence at large distance. When, on average, the defects do not contribute, the layer population and the enclosed topological charge both increase polynomially with distance. In dimension 2, the exponent of the leading terms depend on sum rules satisfied, or not, by the maximum entropy coefficients.