We study the asymptotic null spectrum of Gaussian-weighted tests of univariate normality with estimated location and scale. Closed Hermite coefficients give equations both away from and at the unperturbed poles. Every positive eigenvalue of the fully standardized covariance is simple, and the odd and even eigenvalues alternate strictly. For each unperturbed even pole except the largest, there is exactly one weight parameter at which it belongs to the perturbed even spectrum. These parameters are strictly ordered and converge to the boundary of the parameter interval. A signed total-positivity argument proves simplicity more generally for consecutive Gaussian covariance corrections and positive even integrable weights. We also derive the limiting quadratic forms directly from degenerate kernels at standardized observations. A derivative summability condition controls the complete spectral tail, including signed kernels, and is verified for characteristic-function kernels with a finite fourth weight moment. A real Hilbert-space factorization identifies the observation and Fourier spectra. Numerical calculations assess asymptotic calibration.
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...
We study the annealed complexity of Gaussian random homogeneous polynomials on the (N−1)-dimensional unit sphere in the presence of deterministic perturbations depending on fixed orthonormal vectors and external parameters. We derive variational formulas for the exponential asymptotics of the average number of total cr...
Vanessa Piccolo· The Annals of Applied Probab...· 0 citations
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...
Key properties of a large sparse operator can often be determined by only a small, spectrally localized subset of its eigenmodes. In lattice QCD with Wilson fermions, the sign of the fermion determinant is determined by the parity of the number of eigenvalues lying on the negative real axis of the non-Hermitian Wilson-...
Bhabani Sankar Tripathy, M. Padmanath· 0 citations
We study weak limits of multiple Wiener integrals together with the limits of their kernel contractions. After passage to a subsequence, bounded kernel sequences admit a Gaussian Hermite representation whose coordinates carry weights determined by the original chaos orders. In the limits of kernel contractions, only pa...
Let a normalized continuous Parseval frame describe the phase space of a reproducing kernel Hilbert space. The frame coefficients of an orthonormal family have total mass equal to the number of states and pointwise mass at most one. This elementary exclusion principle gives explicit lower bounds for the total cost of a...
