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Convergence of the Subcritical γ-LQG Metric to the Critical 2-LQG Metric as γ→ 2
Abstract
We show that the γ-LQG metric (appropriately re-normalized) for γ∈ (0,2) converges in law to the critical 2-LQG metric (appropriately re-normalized) with respect to the local uniform topology of continuous functions on ℂ × ℂ. Combining with the results in arXiv:2509.15544, we obtain that the law of the γ-LQG metric (appropriately re-normalized) is continuous in γ∈ [0,2] with respect to the local uniform topology of continuous functions on ℂ × ℂ, where the 0-LQG metric corresponds to the Euclidean metric on ℂ.
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BibTeX
@misc{kavvadias2026convergence,
title = {{Convergence of the Subcritical $γ$-LQG Metric to the Critical 2-LQG Metric as $γ\to 2$}},
author = {Konstantinos Kavvadias},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29361},
eprint = {2608.29361},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29361},
}
RIS
TY - UNPB
TI - Convergence of the Subcritical γ-LQG Metric to the Critical 2-LQG Metric as γ→ 2
AU - Konstantinos Kavvadias
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29361
UR - https://arxiv.org/abs/2608.29361
AB - We show that the γ-LQG metric (appropriately re-normalized) for γ∈ (0,2) converges in law to the critical 2-LQG metric (appropriately re-normalized) with respect to the local uniform topology of continuous functions on ℂ × ℂ. Combining with the results in arXiv:2509.15544, we obtain that the law of the γ-LQG metric (appropriately re-normalized) is continuous in γ∈ [0,2] with respect to the local uniform topology of continuous functions on ℂ × ℂ, where the 0-LQG metric corresponds to the Euclidean metric on ℂ.
ER -