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A certificate for the triangle variational problem

Matthew Kwan, Huy Tuan Pham

Palomar Registrypalomar/PALOMAR-2026-10-19-000018Oct 19, 2026math.COscore 0

A Lean formalization of a technical lemma in the paper "Nonlinear lower-tail large deviations at criticality" by Matthew Kwan and Huy Tuan Pham. This lemma is used to solve a certain variational problem, which is necessary to characterise the probability that a random graph is triangle-free in the so-called "critical regime" where the edge probability is of order 1 / sqrt n. Specifically, this lemma defines a "certificate function" G and proves that it satisfies a certain inequality. This involves lots of interval arithmetic.

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