arXiv:2610.28665v1 Announce Type: new Abstract: For a centered homogeneous generalized Gaussian field with spectral weight $C|\omega|^{-\gamma}$, we prove two-endpoint recovery of normalized posterior wavelet covariances under fixed finite admissible observations. Global dilation symmetry holds if and only if all observation functions vanish. The nonzero wavelet and the observation functions are real Schwartz functions with $M\geq1$ vanishing moments, with $C>0$ and $\gamma<2M+1$. Noise is Gaussian and field-independent, and total observation covariance is positive definite. Under simultaneous dilation of target scales and positions, multiplication by $\lambda^{-\gamma}$ recovers the prior covariance as $\lambda\downarrow0$ and $\lambda\uparrow\infty$, uniformly on every fixed compact target set. If a nonzero observation function exists, additional finite first nonzero Fourier orders $m_\psi,m_i$ at zero of the wavelet and nonzero observation functions yield compact-uniform recovery bounds $O(\lambda^{2m_\psi+1-\gamma})$ and $O(\lambda^{-(2\min_i m_i+1-\gamma)})$, with leading coefficients and cancellation-dependent improvements. The bounds are exact leading orders when their coefficients are nonzero. For the Mat\'ern-type spectrum $S(\omega)=C(\kappa^2+\omega^2)^{-p}$, $\kappa>0$, $1/2Source：https://arxiv.org/abs/2610.28665
My favorites