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arXiv · 2507.16705

Testing the variety hypothesis

A. Lerario·P. Roos Hoefgeest·M. Scolamiero·A. Tamai
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Abstract

Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the variety hypothesis". We prove an upper bound on the so-called "sample complexity" of this problem and show how it can be reduced to a semialgebraic decision problem. This is done by studying in a quantitative way the Hausdorff geometry of the space of real algebraic varieties of a given dimension and degree.

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BibTeXRIS

A. Lerario, P. Roos Hoefgeest, M. Scolamiero, A. Tamai. 2025-07-22. Testing the variety hypothesis. https://arxiv.org/abs/2507.16705

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