On the Expected Depth of Random Circuits
Sunil Arya, Mordecai J. Golin, Kurt Mehlhorn · Combinatorics Probability Computing · 1999
In this paper we analyse the expected depth of random circuits of fixed fanin f. Such circuits are built a gate at a time, with the f inputs of each new gate being chosen randomly from among the previously added gates. The depth of the new gate is defined to be one more than the maximal depth of its input gates. We show that the expected depth of a random circuit with n gates is bounded from above by ef ln n and from below by 2.04 … f ln n.