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Mixing Time of Kac's Walk on the Rotation Group

Probability & statistics · posed by Walk introduced by W. K. Hastings; optimal rate the standing target of the mixing-time literature, 1970 · solved

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Statement

Kac's walk on the rotation group, introduced by Hastings in 1970, is a central high-dimensional Markov chain in statistical physics and computational science. The paper proves it mixes in n2log⁡nn^2 \log n steps, the conjectured optimal rate, closing the gap left by a long line of successive improvements.

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

  1. proof attempt · #1

    Natesh S. Pillai and Aaron Smith, using GPT Pro 5.4

    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.

    "Much of this paper was developed in collaboration with GPT Pro 5.4. In particular, the idea of using matrix martingale inequalities" came from that collaboration. Pillai and Smith are the authors of the previous best bounds for this walk.

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