Author

Chunhao Cai

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Preprint Aug 2026

Closed Response Calculus and Joint Densities for the Liouville Quantum Gravity Metric

We give a general criterion for transferring first-order responses on an underlying probability space to a closed differential calculus on the law of an observable. An integration-by-parts identity removes presentation ambiguity and yields a closable gradient, its divergence, and a closed Markov form. We apply this sch...

Chun-Hao Cai · 0 citations

Preprint Aug 2026

Response Calculus for Spectral Simplicity and Joint Eigenvalue Densities

We develop a perturbative response calculus for spectral problems obtained by changing the speed measure of a fixed symmetric energy form in a Gaussian environment. If Cameron--Martin translation acts by $\mu_{x+f}=e^{\kappa f}\mu_x$, unitary transport identifies the varying $L^2$ spaces and produces a common-domain an...

Chunhao Cai · 1 citation · ⚡1

Preprint Aug 2026

Spectral Simplicity and Joint Eigenvalue Densities for a Non-Gaussian Brownian Time Change

We study a Brownian time change on the unit square whose speed measure is constructed from a Dirichlet eigenfunction expansion with independent non-Gaussian coefficients. For $0<\gamma<\sqrt2$, the measure is obtained by a second-moment martingale argument. Finite coefficient translations induce coherent exponential ti...

Chunhao Cai · 0 citations