  While wealth distribution in the world is highly skewed and heavy-tailed,
human talent - as the majority of individual features - is normally
distributed. In a recent computational study by Pluchino et al [Talent vs luck:
The role of randomness in success and failure, Adv. Complex Syst. 21 (03-04)
(2018) 1850014], it has been shown that the combined effects of both random
external factors (lucky and unlucky events) and multiplicative dynamics in
capital accumulation are able to clarify this apparent contradiction. We
introduce here a simplified version (STvL) of the original Talent versus Luck
(TvL) model, where only lucky events are present, and verify that its dynamical
rules lead to the same very large wealth inequality as the original model. We
also derive some analytical approximations aimed to capture the mechanism
responsible for the creation of such wealth inequality from a
Gaussian-distributed talent. Under these approximations, our analysis is able
to reproduce quite well the results of the numerical simulations of the
simplified model in special cases. On the other hand, it also shows that the
complexity of the model lies in the fact that lucky events are transformed into
an increase of capital with heterogeneous rates, which yields a non-trivial
generalization of the role of multiplicative processes in generating wealth
inequality, whose fully generic case is still not amenable to analytical
computations.
