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Spectral Edge of the Quartic SYK Model

Mathematical physics · posed by 2016 · candidate

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Statement

Determine the leading asymptotic of the largest eigenvalue of the NN-Majorana quartic SYK Hamiltonian as N→∞N \to \infty. The preprint proves λ1/N→4∫0∞g0(t)4 dt≈0.32504\lambda_1/\sqrt{N} \to 4\int_0^\infty g_0(t)^4\,dt \approx 0.32504 almost surely, via the limiting free energy at every fixed positive temperature.

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  1. proof attempt · #1

    Yukun He, using GPT-5.6

    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.

    Developed with GPT-5.6; the finite-bath interpolation reduces the quartic SYK pressure to a local cavity-kernel identity.

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