Upper bound for random correlation 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.

As discussed here, the sampling distribution of correlation for uncorrelated Gaussian variables covers the entire range of $[-1,1]$. While you have not assumed Gaussian variables, you have not ruled out Gaussians. Consequently, the upper bound is $1$, and the lower bound is $-1$.
Even if you do rule our Gaussian variables, the entire range of $[-1,1]$ is possible. Just due to bad luck, which we can quantify using an appropriate sampling distribution, it’s always possible to happen to have perfect positive or negative correlation in the sample, despite zero population correlation.
