**Abstract: **
A finite-dimensional Hilbert space is usually described in terms
of an orthonormal basis, but in certain approaches or applications a
description in terms of a finite overcomplete system of vectors, called a
finite tight frame, may offer some advantages. The use of a finite tight
frame may lead to a simpler description of the symmetry transformations, to
a simpler and more symmetric form of invariants or to the possibility to
define new mathematical objects with physical meaning, particularly in
regard with the notion of a quantization of a finite set. I will present in
this talk the frame quantization of a finite set, its probabilistic aspects,
and possible applications.