http://www.physorg.com/news95074548.html

According to some research, the wealth of the population follows two separate distributions. Scientists from Saha Institute of Nuclear Physics and Institute of Mathematical Sciences have analyzed different sets of data that shows that the poorer majority of the population follows the Gibbs/log-normal distribution, while the wealthiest follow a power law distribution. The power law distribution reflects the “rich get richer.” Data, income tax returns and net value of assets, was taken from a multiple countries including the U.S., UK, Japan, and India. Also data was taken from 19^th century Europe. Surprisingly, all this data showed the same conclusion that the lower 90% of the population, in terms of income, followed a log-normal distribution. As income increased, there is an initial rapid rise in population followed by a rapid decline. The wealthiest 10% followed a Pareto power law. Interestingly, the Gibbs distribution that the poorest 90% of the population follow is also the distribution of energy in an ideal gas in equilibrium. This is because, on the global level as scientists say, the exchange of assets and the scattering of molecules are both random. The help of these models can lead to more equitable distribution of wealth.

The “rich get richer” phenomenon explains the reason why only the top 10% of the wealthiest individuals follow a power law. This phenomenon says that typically the largest increase in wealth is attributed to the richer part of the population; therefore, increasing the gap between the rich and the poor. As the article implies that the exchange of assets on the global level is random, the Gibbs distribution, however, applies only to the lower 90% of the population. Neither of these two things is intuitive and is actually quite interesting. The reason lies with the “rich get richer” theory that is present in a lot of places such as networks or popularity of books. The theory of the richest “nodes” growing the fastest is what leads to the power law distribution. The most popular person/object will gain popularity the fastest because the most people know about him/it. However, this distribution fails after the top 10% where the “randomness” of asset trading on the global level becomes more of a factor than the “rich getting richer.”