Large Deviation Principles for Area of Quantum Disks with Unit Left Boundary Length

Yuchen Fan; Zhenfeng Tu

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arXiv · 2610.02531

Large Deviation Principles for Area of Quantum Disks with Unit Left Boundary Length

Yuchen Fan·Zhenfeng Tu

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Abstract

We prove a large deviation principle for the area of a two-pointed weight-$W$ quantum disk conditioned to have left boundary length one, where $0<W<2$ is fixed and $γ\downarrow0$ without a subsequence restriction. Conformal welding and the one-block mating-of-trees law give independent Brownian blocks and a recursive area decomposition. Growing moments and negative Laplace transforms lead to two Hamilton--Jacobi equations, whose characteristic solutions determine the limiting transforms. Direct comparison proves moment convergence; compact-interval comparison and a change of measure prove Laplace convergence. The resulting good rate function is specified by scalar endpoint equations and is elementary when $W=1$.

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Yuchen Fan, Zhenfeng Tu. 2026-10-01. Large Deviation Principles for Area of Quantum Disks with Unit Left Boundary Length. https://arxiv.org/abs/2610.02531

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