To be specific: if $G$ is a finite group and $\operatorname{Irr}(G)$ the set of its irreducible characters (over the complex field) then we know that $$ 1 = \sum_{\phi \in {\rm Irr}(G)} \frac{(d_\phi)^2}{|G|} $$ where $d_\phi=\phi(e)$ is the degree of the character $\phi$. Thus we get a probability measure on $\operatorname{Irr}(G)$ which assigns mass $|G|^{-1}(d_\phi)^2$ to the atom $\{\phi\}$.
My question is: among finite group theorists, what is the usual name for this measure? I need to know since I am writing a paper which might include this audience, and I don't wish to clash with the accepted conventions unless it's necessary.
I think that in the context of e.g. random Young diagrams and representations of the symmetric group, this is sometimes referred to as "Plancherel measure". However, for a non-commutative harmonic analyst, it is traditional and more natural to use "Plancherel measure" for the measure $\nu$ on the dual of a (Type I, unimodular) locally compact group $G$ which makes the Plancherel formula hold $$ \int_G \lvert f(x)\rvert^2 \,dx = \int_{\widehat{G}} \lVert \pi(f) \rVert_{\rm HS}^2\,d\nu(\pi) $$ Note that with this convention, if $G$ is finite then $\nu(\{\phi\})=|G|^{-1} d_\phi$, and so $\nu$ is usually not a probability measure.
