Before revision:  We also calculate the distribution of the optimal weights over the random samples and show that the regularizer preferentially removes the assets with large variances, in accord with one's natural expectation . The analytic calculations are supported by numerical simulations. The analytic and numerical results are in perfect agreement for N/T<2, but some numerical solvers keep yielding a stable solution even in the region N/T>2. This is because there are regularizers built into these solvers that stabilize the otherwise freely fluctuating, meaningless solutions .
After revision:  We also calculate the distribution of the optimal weights over the random samples and show that the regularizer preferentially removes the assets with large variances, in accord with one's natural expectation .