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We define a group with local data over a number field $K$ as a group $G$together with homomorphisms from decomposition groups ${\rmGal}(\overline{K}_p/K_p)\to G$. Such groups resemble Galois groups, justwithout global information. Motivated by the use of random groups in the studyof class group statistics, we use the tools given by Sawin-Wood to construct arandom group with local data over $K$ as a model for the absolute Galois group${\rm Gal}(\overline{K}/K)$ for which representatives of Frobenius aredistributed Haar randomly as suggested by Chebotarev density. We utilize Law ofLarge Numbers results for categories proven by the author to show that this isa random group version of the Malle-Bhargava principle. In particular, itsatisfies number field counting conjectures such as Malle's Conjecture undercertain notions of probabilistic convergence including convergence inexpectation, convergence in probability, and almost sure convergence. Theseresults produce new heuristic justifications for number field countingconjectures, and begin bridging the theoretical gap between heuristics fornumber field counting and class group statistics.

A Random Group with Local Data Realizing Heuristics for Number Field Counting