Resolution limits of analytic continuation from imaginary-time data

Given $G(\tau) = \int \mathrm{d}w\, K(\tau, w) A(w)$ with $K = \exp(-\tau w)/(1 + \exp(-\beta w))$ on $0 \le \tau \le \beta$ and Gaussian noise of size $\sigma$, determine the optimal resolution of the spectral function $A(w)$ (minimal resolvable width and amplitude of a feature at frequency $w$) as a function of $\sigma, \beta \text{ and } w$, and construct estimators (maximum entropy, stochastic, Nevanlinna, Bayesian) with certified error bounds that reach it. An answer is proven bounds plus an estimator attaining them on benchmarks.

A theorem bounding achievable resolution from below and an estimator whose certified intervals match that bound on test spectra.