spur-cor

set.seed(123)
max_corrs <- function(d, n = 60, n_iter = 1000)
    replicate(n_iter, {
        m <- matrix(rnorm(n * d), ncol = d)
        max(cor(m)[-1, 1])
    })

r1 <- data.frame(d = 800, r = max_corrs(800))
r2 <- data.frame(d = 6400, r = max_corrs(6400))
r <- rbind(r1, r2)

ggplot2::ggplot(r, aes(x = r, fill = factor(d), alpha = 0.5)) +
    ggplot2::geom_density() +
    ggplot2::scale_alpha(guide = "none") +
    ggplot2::labs(fill = "Dimensions")