# representation theory – Distribution of dimensions of \$S_n\$ irreps for large \$n\$

A histogram of the dimensions of the irreps of $$S_n$$ becomes sharply peaked. For example, here is a log histogram for $$S_{50}$$:

Most of the dimensions of $$S_{50}$$ have 26-29 decimal digits.

Is the asymptotic form of this distribution for large $$n$$ known?