A New Approach to Personal Income Distribution
  The results of R^2 dynamical random surface model (2-dimensional quantum gravity with a $R^2$ term) are applied to explain the personal income distribution. A scale invariance exists if there is not the $R^2$ term in the action. The R^2 term provides a typical scale and breaks the scale invariance explicitly in the low and middle income range. A new distribution, Weibull distribution, is deduced from the action analytically in the low income range, and a consistent fitting is obtained in the whole income range. Also, we show that the lognormal distribution in the middle income range can be understood in this framework. 
Atushi Ishikawa, Tadao Suzuki and Masashi Tomoyose