This is the conclusion of Thomas Picketty's 2013 book, "Capital in the 21st Century." Due to the historical averages of the rate of return on capital, he concluded empirically that wealth will continue to concentrate to the point to inheritors, to the extent that individuals become increasingly unable through labor to achieve parity to the inheritors.
The book was very provocative in economist circles, but even the critics mostly lauded the empirical work at collecting historical data. https://en.wikipedia.org/wiki/Capital_in_the_Twenty-First_Ce...