I am reading some heavy hitter (HH) papers when I run into the following reduction theorem. The theorem attempts to reduce an HH problem with a very small tail frequency $\epsilon$ to multiple HH instances with higher tail frequencies.
More precisely, the reduction utilizes a random hash function $h$ that throws an item index $i \in [n]$ to one of the $z$ bins. Each bin will then become an HH instance.
The problem is, how do we know whether or not each of the $z$ bins contains roughly $1/z$ of the heavy hitters? The paper then claims in (2) that, the probability that one of the bin contains more than $C \log(1/\delta)$ heavy hitters is less than $\delta/3$.
My Question
How to prove (2) using Chernoff bound, as is suggested by the paper?
