Asymptotics for push on the complete graph

We study the classical randomized rumour spreading protocol push. Initially, a node in graph possesses some information, which is then spread round based manner. In each round, informed chooses uniformly at random one of its neighbours and passes information to it. The central quantity interest runtime, that is, number rounds needed until every has received information. push variations it have been studied extensively. Here we case where underlying complete with n nodes. Even this most basic setting, specifying limiting distribution statistics remained open problems since was introduced. our main result describe runtime. show does not converge, becomes, after appropriate normalization, asymptotically periodic both on log2n as well lnn scale. Additionally, suitable subsequences determine expected runtime higher moments