The rich will get richer because return on investment

Most of leftist will say that, for example if someone has 20% of global wealth in a free economy there is no way he will loose it, nor he will stop being the richest person in the world, him or his sons. Cause he has to spend les % of money than anyone else so he can invest much more. I know this is not true based on empirical evidence, but I have a hard time rebutting this based solely on logic. I know someone can come up with an idea that will make a lot of wealth (google, apple...) but I'm not sure how generation after generation they can reduce this 20% if they invest in a diversified portfolio that give him a return, even if is 1% (with no inflation). Can anyone point me on the right direction? I have a theory although I'm not sure if it's true: The richest person will increase his purchasing power while reducing his net worth because the difficulty of successfully investing so much money (you can make a lot of return if you're poor and open a small company after you see a need for a particular market but this becomes increasingly difficult if you want the same return when you have a lot of money).

link: http://ift.tt/1TImRsf