PreprintCC BY 4.0HAL
The positive-curvature semiclassical limit
Abstract
We prove a good large deviation principle for the scaled unit-area Liouville field on the sphere, in the positive curvature regime and assuming the strict Troyanov condition. The rate function is the renormalized classical Liouville action minus its minimum. Consequently, the field concentrates exponentially at the unique unit-area metric of constant positive curvature with the prescribed conical singularities. The proof combines a joint field-mass large deviation principle with moment bounds that control the positive GMC tilt imposing unit area. This resolves the positive-curvature semiclassical conjecture of Lacoin, Rhodes, and Vargas in this regime.
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BibTeX
@misc{fan2026positivecurvature,
title = {{The positive-curvature semiclassical limit}},
author = {Yuchen Fan and Zhenfeng Tu},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05838591v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The positive-curvature semiclassical limit
AU - Yuchen Fan
AU - Zhenfeng Tu
PY - 2026
DA - 2026/10/25
PB - HAL
UR - https://hal.science/hal-05838591v1
AB - We prove a good large deviation principle for the scaled unit-area Liouville field on the sphere, in the positive curvature regime and assuming the strict Troyanov condition. The rate function is the renormalized classical Liouville action minus its minimum. Consequently, the field concentrates exponentially at the unique unit-area metric of constant positive curvature with the prescribed conical singularities. The proof combines a joint field-mass large deviation principle with moment bounds that control the positive GMC tilt imposing unit area. This resolves the positive-curvature semiclassical conjecture of Lacoin, Rhodes, and Vargas in this regime.
ER -