Write an equation showing a condition indicating correlation between two variables

I am trying to write this conditional equation:

I am not sure what could be the mathematical syntax for saying:

"variables x and y are correlated".

While searching for this, I came to know that it is really tough to find such a thing. Please let me know if you aware of such a mathematical syntax.

In addition, I am also curious to know how would following be written in an equation.

1. "variables x and y are anti-correlated"

2. "variables x and y are significantly correlated"

3. "variables x and y are correlated, while accounting for a covariate z"

4. "variables x and y are correlated based on ranks" (as in Spearman’s correlations)