INFINITE-DIMENSIONAL L´EVY AREA: PROBABILITY-SELECTED CRITICAL GEOMETRY AND SHARP SPECTRAL SELECTION

INFINITE-DIMENSIONAL L´EVY AREA: SHARP OPERATOR-IDEAL REGULARITY AND ANISOTROPIC IT ˆO GEOMETRY

High-Dimensional Spectral Limits for Gaussian KL-Unbalanced Optimal Transport

We study high-dimensional random-matrix limits of Gaussian Kullback--Leibler unbalanced optimal transport (KL-UOT). Under equal marginal penalties, the covariance action admits an exact log-determinant representation in terms of a nonlinear ridge product, together with a positive-semidefinite extension that remains fin...

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...

Fractional Wiener chaos: Part 2. Interface spectral chaos

We construct a product spectral decomposition from power-normalised parabolic-cylinder functions. At noninteger real orders, these functions are not square integrable with respect to the corresponding full-line Gaussian measure. Bringing the admissible half-line branches into the same Gaussian space and matching them a...

Spectral gap for the three-dimensional damped cubic wave equation with degenerate noise

We establish a weighted Wasserstein spectral gap for the three-dimensional damped cubic wave equation with genuinely finite rank Brownian forcing. Under a saturation condition, the gap holds with respect to the negative phase topology $\mathcal E_s=H^{-s}\times H^{-1-s}$ for every $0<s<1/2$, from which we deduce unique...

Sharp spectral-scale stability for parabolic equations with measure-valued delay

We study the dependence of parabolic solution operators on a finite signed measure describing the delay law. For a positive self-adjoint generator with compact inverse, a weighted dyadic spectral sum characterizes the norm of the semigroup-integrated memory perturbation. An exact realization identity transfers the matc...