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arXiv · 2610.37549

Nonlinear uncertainty principle

Alex Cohen·Semyon Dyatlov
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Abstract

We prove an uncertainty principle for subsets of $\mathbb R$ under weak branching assumptions. We impose a nonlinearity condition on the phase; without it our uncertainty principle fails e.g. for arithmetic progressions. The key ingredient in the proof is Shmerkin's nonlinear projection theorem. This paper is a part of a work in progress, but it is released earlier than the rest of that paper since it is also used in a paper of Cohen-Li-Tao. It also has an overlap with our recent paper [arXiv:2609.30261]; see the end of the introduction for more details.

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Alex Cohen, Semyon Dyatlov. 2026-10-27. Nonlinear uncertainty principle. https://arxiv.org/abs/2610.37549

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