I recently had a conversation with a college of mine and this question popped into my mind and I am unsure how to solve it.
Let's say I have 100 variables. Some of the variables have a pairwise relationship but most of them do not and are just random.
My question is what amount of correlation can I expect that is just due to randomness?
How would I go about calculating an upper bound of correlation due to randomness?
Any help or pointing in a direction would be greatly appreciated.