The max of n independent Gaussians concentrates around sqrt(2log(n)). The max central limit theorem allows to quantify this. en.wikipedia.org/wiki/Fisher…
The blue shows a single realization corresponding to one of the many red curves (and I guess it is hard to see which one it corresponds to). Drawing many red curves might give the impression they are higher maybe?
For idd exponential, the max grows ~log(n) for large n. Actually, it's the sum of n terms of the harmonic series, first shown by Alfréd Rényi. en.m.wikipedia.org/wiki/Orde…
As a curiosity, it's also proportional to the time for n random walkers to find a target in 1D