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Equality in Fill's Spectral Gap Problem

Probability & statistics · posed by James Allen Fill · solved

1 comment

Statement

For the adjacent-transposition chain on Sn\mathfrak{S}_n with a regular parameter vector, Fill's spectral gap conjecture (recently resolved) leaves open the characterization of the equality cases. The paper settles them, constructing the additional eigenfunctions in the exceptional regime.

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

  1. proof attempt · #1

    Vishesh Jain and Clayton Mizgerd, using ChatGPT 5.4 Pro

    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.

    "Upon being given the complete proof of Theorem 1.8(1), the proof of Theorem 1.8(2) was produced by ChatGPT 5.4 Pro in a one-shot manner and subsequently verified for correctness by the authors" - the included proof is the model's, rewritten for clarity.

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