The center of the distribution always has the highest density, but the ratio of 'probability mass close to centroid' / 'total probability mass' drops off as num

The center of the distribution always has the highest density, but the ratio of 'probability mass close to centroid' / 'total probability mass' drops off as number of dimensions grows. This is somewhat related to another 'curse of dimensionality' observation, which is that the volume of a hyperball / volume of hyperspace tends towards zero as dimensions grow -- there's just a lot more volume that's in some sense 'far' from the center.