What is a short hand for random variable X, Y independent?

Question

In some of the textbook problems, it would say, suppose X and Y are zero mean, unit variance independent Gaussians...

I would usually just write $$X,Y \sim \mathcal N(0,1)$$ and this is a nice short hand form of this sentence, but how do I express independence? I used to write COV(X,Y) = 0 until I realized that COV(X,Y) = 0 does not imply independence

Answer 1

You often see "i.i.d." used for "independent identically distributed". So you could write $$X,Y \textrm{ i.i.d.} \sim \mathcal N(0,1)$$

Answer 2

I've had several profs who sometimes write $X\perp Y$ to mean $X$ and $Y$ are independent.