[D] Literature on embeddings from metric space to L2 space?

I'm currently trying to find theory papers on metric embeddings (namely, metric space to L2 space embeddings). I've been able to find literature on the distortion (albeit these results are old) such as [this](http://www-math.mit.edu/~goemans/18409-2006/lec2.pdf), but I haven't been able to find more specific studies that answer questions such as:

* Given a D-embedding into L2 space, how much distortion can we expect on average given certain conditions? (e.g. we know lower bound for distortion for metric -> L2 space is …

l2 literature machinelearning space