I will talk on a generalization of classical Calabi's strong maximum (1957) in the framework of Dirichlet forms associated with strong Feller diffusion processes.
The proof is stochastic and the result can be applicable to a singular geometric space appeared in the measured Gromov-Hausdorff convergence (precisely in the convergence by spectral distance by Kasue Kumura) of compact Riemannian manifolds with uniform lower Ricci curvature and uniform upper diameter.