Assess the optimality of explicit positivity filtering of Ritz values in noisy analyses

Determine whether explicitly discarding negative Ritz values (imposing positivity to reflect the positive‑definite transfer matrix in the infinite‑statistics limit) is the optimal strategy for practical analyses of noisy lattice QCD correlator matrices, given the potential for small eigenvalues to fluctuate negative and for clipping at zero to bias error analysis.

Background

In noisy data settings, some Ritz values can be negative, even though the true transfer matrix is positive‑definite. A straightforward approach is to filter on positivity and discard negative Ritz values.

However, the authors explicitly note uncertainty about whether this strategy is best in practice, since oscillatory contributions may be noise‑related but small negative fluctuations can occur and clipping at zero may complicate uncertainties.