Generic sum rules express arbitrary traces through convolutions of a single Laguerre polynomial for group character averages in Gaussian matrix models.
Spectral form factor and semi-circle law in the time direction
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abstract
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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hep-th 1years
2026 1verdicts
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Group character averages via a single Laguerre
Generic sum rules express arbitrary traces through convolutions of a single Laguerre polynomial for group character averages in Gaussian matrix models.