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  "problem_id": "vibemathed:kac-walk-rotation-mixing",
  "title": "Mixing Time of Kac's Walk on the Rotation Group",
  "canonical_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 $n^2 \\log n$ steps, the conjectured optimal rate, closing the gap left by a long line of successive improvements.",
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      "title": "arXiv",
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      "attempted_at": "2026-04-26T00:00:00.000Z",
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        "Natesh S. Pillai",
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      "prompt_public": null,
      "outcome": "\"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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