Optimal growth entails risky localization in population dynamics

DISAT, Politecnico Corso Duca degli Abruzzi - I-10129 Torino, Italy

Received: 31 January 2018
Accepted: 27 April 2018

Abstract

Essential to each other, growth and exploration are jointly observed in alive and inanimate entities, such as animals, cells or goods. But how the environment's structural and temporal properties weights in this balance remains elusive. We analyze a model of stochastic growth with time correlations and diffusive dynamics that sheds light on the way populations grow and spread over general networks. This model suggests natural explanations of empirical facts in econo-physics or ecology, such as the risk-return trade-off and the Zipf law. We conclude that optimal growth leads to a localized population distribution, but such risky position can be mitigated through the space geometry. These results have broad applicability and are subsequently illustrated over an empirical study of financial data.