Maximum bin load for $\alpha n$ balls into $n$ bins

Question

In a paper I am reading the author writes:

A standard result concerning balls and bins shows that if we throw at least $\alpha n$ balls into at most $n$ bins, then the maximum bin load is $(1+o(1))\frac{\ln n}{\ln \ln n}$ with high probabilty.

Does anyone know how to see this or where I could read a proof?

Thanks!