Quantitative analytic stable regularity

G. Conant; C. Terry

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arXiv · 2607.21762

Quantitative analytic stable regularity

G. Conant·C. Terry

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Abstract

We prove quantitative stable regularity lemmas for binary real-valued functions, extending the work of Malliaris and Shelah for stable graphs. The statements of our results are modeled after non-quantitative theorems for stable functions due to Chavarria, Conant, and Pillay. One of the key tools in our quantitative proof is an "analytic symmetry lemma", which gives a function-theoretic analogue of the fact that a pair of good sets in a graph has density close to 0 or 1. We also develop a function-theoretic treatment of Malliaris and Shelah's random sampling method for refining partitions consisting of good sets into equipartitions.

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BibTeX RIS

G. Conant, C. Terry. 2026-07-23. Quantitative analytic stable regularity. https://arxiv.org/abs/2607.21762

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