  We obtain a sufficient condition for benign overfitting of linear regression
problem. Our result does not rely on concentration argument but on small-ball
assumption and thus can holds in heavy-tailed case. The basic idea is to
establish a coordinate small-ball estimate in terms of effective rank so that
we can calibrate the balance of epsilon-Net and exponential probability. Our
result indicates that benign overfitting is not depending on concentration
property of the input vector. Finally, we discuss potential difficulties for
benign overfitting beyond linear model and a benign overfitting result without
truncated effective rank.
