  Under the Heisenberg evolution in chaotic quantum systems, initially simple
operators evolve into complicated ones and ultimately cover the whole operator
space. We study the growth of the operator ``size'' in this process, which is
related to the out-of-time-order correlator (OTOC). We derive the full time
evolution of the size distribution in large $N$ quantum mechanics of Majorana
fermions. As examples, we apply the formalism to the Brownian SYK model
(infinite temperature) and the large $q$ SYK model (finite temperature).
