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A useful heuristic in the understanding of large random combinatorialstructures is the Arratia-Tavare principle, which describes an approximation tothe joint distribution of component-sizes using independent random variables.The principle outlines conditions under which the total variation distancebetween the true joint distribution and the approximation should be small, andwas successfully exploited by Pittel in the cases of integer partitions and setpartitions. We provide sufficient conditions for this principle to be true in ageneral context, valid for certain discrete probability distributions which are$\textit{perturbed log-concave}$, via a quantitative local central limittheorem. We then use it to generalize some classical asymptotic statistics incombinatorial theory, as well as assert some new ones.

A robust quantitative local central limit theorem with applications to enumerative combinatorics and random combinatorial structures