  We investigate the generic aspects of quantum coherence guided by the
concentration of measure phenomenon. We find the average relative entropy of
coherence of pure quantum states sampled randomly from the uniform Haar measure
and show that it is typical, i.e., the probability that the relative entropy of
coherence of a randomly chosen pure state is not equal to the average relative
entropy of coherence (within an arbitrarily small error) is exponentially small
in the dimension of the Hilbert space. We find the dimension of a random
subspace of the total Hilbert space such that all pure states that reside on it
almost always have at least a fixed nonzero amount of the relative entropy of
coherence that is arbitrarily close to the typical value of coherence. Further,
we show, with high probability, every state (pure or mixed) in this subspace
also has the coherence of formation at least equal to the same fixed nonzero
amount of the typical value of coherence. Thus, the states from these random
subspaces can be useful in the relevant coherence consuming tasks like
catalysis in the coherence resource theory. Moreover, we calculate the expected
trace distance between the diagonal part of a random pure quantum state and the
maximally mixed state, and find that it does not approach to zero in the
asymptotic limit. This establishes that randomly chosen pure states are not
typically maximally coherent (within an arbitrarily small error). Additionally,
we find the lower bound on the relative entropy of coherence for the set of
pure states whose diagonal parts are at a fixed most probable distance from the
maximally mixed state.
