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Stable Phase Retrieval for Spans of Independent Random Variables

Analysis · posed by Calderbank, Daubechies, Freeman and Freeman · solved

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Statement

After L2L^2 normalization, stable phase retrieval holds over the L2L^2-spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided L1L^1 bound. This confirms the characterization conjectured by Calderbank, Daubechies, Freeman and Freeman.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Pedro Abdalla, Jaume de Dios Pont, João P. G. Ramos and Mitchell A. Taylor, using GPT-5 + Claude Opus 4

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

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