Stable Phase Retrieval for Spans of Independent Random Variables
Statement
After normalization, stable phase retrieval holds over the -spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided bound. This confirms the characterization conjectured by Calderbank, Daubechies, Freeman and Freeman.
Context
Confirms a characterization conjectured by the authors of the foundational work on stable phase retrieval, and does so completely rather than in special cases.
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Under a heading on the usage of large language models, the authors say the models played a significant role in the development of the work, describing arguments proposed by the authors and then found by GPT-5, with Claude Opus 4 also used.
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