On low frequency inference for diffusions without the hot spots conjecture

We remove the dependence on the ‘hot-spots’ conjecture in two of the main theorems of the recent paper of Nickl (2024). Specifically, we characterise the minimax convergence rates for estimation of the transition operator P_{f} arising from the Neumann Laplacian with diffusion coefficient f on arbitrary convex domains with smooth boundary, and further show that a general Lipschitz stability estimate holds for the inverse map P_{f} \mapsto f from H^{2} \to H^{2} to L^{1} .