The second term in the spectral expansion of the expected LQG heat trace as t to 0 is governed by the KPZ exponent.
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2026 2verdicts
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Introduces slowed-down Gaussian fields (including 1D branching Brownian motions in cooling environments) and proves tightness of maxima with growth T^{1-α} and phase transition at α=1/3.
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Spectral expansion of LQG heat trace and KPZ scaling
The second term in the spectral expansion of the expected LQG heat trace as t to 0 is governed by the KPZ exponent.
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Extrema of microscopically slowed-down Gaussian fields
Introduces slowed-down Gaussian fields (including 1D branching Brownian motions in cooling environments) and proves tightness of maxima with growth T^{1-α} and phase transition at α=1/3.