If one assumes that the wealthy are using their money to buy commodities and selling those commodities with the expectation of getting their initial money back plus some delta, then it becomes fairly trivial to demonstrate that the more money you start with the more money gets concentrated around you.
For example, I could leverage my current house to purchase a rental property in my city and rent it at a profit. Over time I'd pay down my loans and the value of my two homes would increase. I could then leverage two properties to purchase more or larger rental properties. My wealth would increase because I had sufficient wealth to begin with.