generating random covariance matrices (with a uniform distribution of correlations)

Petr,
This is the code I used for your suggestion:

	k<-6;kk<-(k*(k-1))/2
	x<-matrix(0,5000,kk)
	for(i in 1:5000){
	A.1<-matrix(0,k,k)
	rs<-runif(kk,min=-1,max=1)
	A.1[lower.tri(A.1)]<-rs
	A.1[upper.tri(A.1)]<-t(A.1)[upper.tri(A.1)]
	cors.i<-diag(k)
	t<-.001-min(Re(eigen(A.1)$values))
	new.cor<-cov2cor(A.1+(t*cors.i))
	x[i,]<-new.cor[lower.tri(new.cor)]}
	hist(c(x)); max(c(x)); median(c(x))

This, unfortunately, does not maintain the desired distribution of
correlations.

I see. I overlooked that you require correlations and not
covariances.

The distribution of correlations cannot be chosen arbitrarily,
since it is not possible to have k variables, such that each
two of them have correlation less than -1/(k-1). For example,
it is not possible that all pairs among 3 variables have
correlation less than -0.5.

The reason is as follows. If X_1, ..., X_k have mean 0,
variance 1 and all pairs have correlation at most c, then

  E (X_1 + ... + X_k)^2 <= k(1 + (k-1)c)

If c < -1/(k-1), then the right hand side is negative,
which is not possible.

Can you relax the requirement on the negative correlations?

Petr.