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Anomalous scaling limit of a Brownian particle in a log-correlated potential

Scott Armstrong, Ahmed Bou-Rabee, Tuomo Kuusi

Palomar Registrypalomar/PALOMAR-2026-10-11-000009Oct 11, 2026math.PRscore 0

A Lean 4 formalization of the paper "Anomalous scaling limit of a Brownian particle in a log-correlated potential" by Armstrong, Bou-Rabee and Kuusi: the subdiffusive scaling limit of a Brownian particle whose drift is the gradient of a log-correlated random potential (Theorem A, in its introduction form and in its precise quenched form), quantitative homogenization of the Dirichlet problem uniformly in the infrared cutoff (Theorem B), and large-scale Hölder regularity with a Liouville theorem (Theorem C), together with the supporting coarse-graining, elliptic-regularity and Markov-process…

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