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Equality in Fill's Spectral Gap Problem

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fill-spectral-gap-equalityProbability & statisticsposed by James Allen Fillrecorded: solved

1 attempt · no person has looked

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.

Context

The equality case of Fill's named spectral gap conjecture, a documented question of the card-shuffling literature.

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1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT 5.4 Pro with Vishesh Jain, Clayton Mizgerd ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    ChatGPT 5.4 Pro
    people
    Vishesh Jain, Clayton Mizgerd

    "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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