Notation for $X - \mathbb{E}(X)$? Let $X$ be a random variable with expectation value $\mathbb{E}(X)=\mu$.
Is there a (reasonably standard) notation to denote the "centered" random variable $X - \mu$?
And, while I'm at it, if $X_i$ is a random variable, $\forall\,i \in \mathbf{n} \equiv \{0,\dots,n-1\}$, and if $\overline{X} = \frac{1}{n}\sum_{i\in\mathbf{n}} X_i$, is there a notation for the random variable $X_i - \overline{X}$?  (This second question is "secondary".  Feel free to disregard it.)

I've never seen any specific notation for these.  They are such simple expressions that there wouldn't be much to gain by abbreviating them further.  If you feel you must, you could invent your own, or just say "let $Y = X - \mu$".
One way people often avoid writing out $X - \mu$ is by a statement like "without loss of generality, we can assume $E[X] = 0$" (provided of course that we actually can).
