we will study complete ricci-flat manifolds with euclidean volume growth. in the case when a tangent cone at infinity of the manifold has smooth cross section, the green function for the laplace equation can be used to define a functional which measures how fast the manifold converges to the tangent cone. using the Łojasiewicz inequality of colding-minicozzi for this functional, we describe how two arbitrarily far apart scales in the manifold can be identified in a natural way. i will also discuss a matrix harnack inequality for the green function when there is an additional condition on sectional curvature, which is an analogue of various matrix harnack inequalities obtained by hamilton and li-cao in time-dependent settings.