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Total Variation for the Lamplighter Walk on Z

Probability & statistics · posed by 2025 · solved

2 comments

Statement

For the switch-walk-switch walk on Z2≀Z\mathbb{Z}_2 \wr \mathbb{Z} started at (0,0)(0,0) and (0,2)(0,2), prove ∥Ptx−Pty∥TV≍t−1/2\|P_t^x - P_t^y\|_{TV} \asymp t^{-1/2}.

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

  1. proof attempt · #1

    QED (GPT-5.5)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    Proved by the QED multi-agent system in decomposition mode; the expert who posed the problem provided no mathematical input beyond the statement.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed expert verification (imported)

    scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here

    Verified by the contributing domain expert; documented in the QED system paper.

    Repeated from the source; nothing was checked here.

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