There is a very interesting model for wealth distribution (the so called yard sale model). You can find a excellent article about it here [1]. Essentially with very basic assumptions you end up with a system that results in a phase transition, where after some point (or if you make small changes of the parameters) wealth just comes completely unequally distributed (an oligarchy).

Someone implemented the simulation for this as well so you can play around with it here [2]. It is definitely very interesting and shows how essentially a small element of luck will result in a situation where a single person becomes the owner of all wealth.

[1] https://www.scientificamerican.com/article/is-inequality-ine...

[2] http://www.physics.umd.edu/hep/drew/math_general/yard_sale.h...