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arxiv: 1811.09988 · v2 · submitted 2018-11-25 · ✦ hep-th

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Spectral form factor and semi-circle law in the time direction

Kazumi Okuyama
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classification ✦ hep-th
keywords rampslopetimefactorformsemi-circlespectralcall
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We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite $N$ with non-zero inverse temperature. Using this exact result, we confirm numerically that the slope of ramp exhibits a semi-circle law as a function of time.

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  1. Group character averages via a single Laguerre

    hep-th 2026-02 unverdicted novelty 6.0

    Generic sum rules express arbitrary traces through convolutions of a single Laguerre polynomial for group character averages in Gaussian matrix models.