Theory of Zipf's Law and Beyond by Yannick Malevergne, Alexander I. Saichev, Didier Sornette. Author Yannick Malevergne, Alexander I. Saichev, Didier Sornette. First, we show that combining Gibrat's law at all rm levels with random processes of rm's births and deaths yield Zipf's law under a "balance" condition between a rm's growth and death rate.
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