  Recent results suggest that the use of ensembles in Statistical Mechanics may
not be necessary for isolated systems, since typically the states of the
Hilbert space would have properties similar to the ones of the ensemble.
Nevertheless, it is often argued that most of the states of the Hilbert space
are non-physical and not good descriptions of realistic systems. Therefore, to
better understand the actual power of typicality it is important to ask if it
is also a property of a set of physically relevant states. Here we address this
issue, studying if and how typicality emerges in the set of matrix product
states. We show analytically that typicality occurs for the expectation value
of subsystems' observables when the rank of the matrix product state scales
polynomially with the size of the system with a power greater than two. We
illustrate this result numerically and present some indications that typicality
may appear already for a linear scaling of the rank of the matrix product
state.
