Open Research Index

HighContrastHomogenization

Scott Armstrong, Tuomo Kuusi, Amélie Loher

Palomar Registrypalomar/PALOMAR-2026-09-25-000016Sep 25, 2026math.APscore 0

A Lean formalization of "Homogenization at a polynomial scale in high contrast" by Armstrong, Kuusi and Loher. The paper studies elliptic equations in random media whose conductivity can vary greatly. It proves that their large-scale behavior becomes predictable at a length bounded by a polynomial in the parameters measuring contrast and randomness, improving earlier bounds. The formalization includes quantitative convergence estimates, approximation by an effective constant-coefficient equation, and large-scale regularity results. It builds on the CoarseGraining library.

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