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arXiv · 2608.27321

A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations

Floris van Doorn·Polona Durcik·Joris Roos·Lenka Slavíková·Christoph Thiele
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Abstract

This blueprint serves as a companion to a forthcoming, shorter traditional mathematical paper. The purpose of this blueprint is two-fold: first, it has served as the foundation for a formalization in Lean 4 of these results. This formalization has been completed largely automatically, making essential use of current frontier large language models. Second, it will serve as a resource to readers of the main paper who are interested in further technical details of the proofs. The main result concerns norm-variation estimates for multiple ergodic averages associated with $n\ge 2$ commuting measure preserving transformations, providing a quantitative strengthening of Tao's norm-convergence theorem and answering an open question of Avigad and Rute. At the core of the analysis lies an explicit real-variable estimate for twisted multilinear averages that is closely related to certain singular Brascamp--Lieb inequalities.

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Floris van Doorn, Polona Durcik, Joris Roos, Lenka Slavíková, Christoph Thiele. 2026-08-27. A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations. https://arxiv.org/abs/2608.27321

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