Random Vandermonde matrix

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I would like to analyze (behavior on condition number, distribution of eigen values etc) random Vandermonde matrices:

$$ V_{i,j} = \alpha_i^{j-1} $$

where $\alpha_i$ are correlated random variables. For simplicity, I can assume they are Gaussian and for simplicity I can assume $\in \mathbb{R}$ (which I would like to extend later to $\mathbb{C}$).

I found some material by Gabriel Tucci (http://ect.bell-labs.com/who/gtucci/publications/vander_final.pdf) for the case when the magnitude is one but I am specifically interested in the case when the magnitude of the variables is not one. Any pointer?