"Balls into Bins" - A Simple and Tight Analysis

Suppose we sequentially throw m balls into n bins. It is a natural question to ask for the maximum number of balls in any bin. In this paper we shall derive sharp upper and lower bounds which are reached with high probability. We prove bounds for all values of m(n) ≥ n=polylog(n) by using the simple and well-known method of the first and second moment.