What kind of power wakes up electrostatic speakers

You need high current for the reasons Audiokinesis so aptly stated above. However, high voltage is necessary as well and that is why tubes generally are a good match with stators, as Sean so rightly points out. The Innersound amps, though a little roughshot in their interpretation will do well, so do the Wolcotts with their better transformers, if not so much in the highs, defenitely excellent in their bass rendering and if you want to spend some more, the Jadis 200 is wonderful and liquid on most stators and if you want to go SS, the Spectral 360, but also their old 200 are both dynamic as well as refined. And yes, before I forget, I have an ancient Threshold Stasis, still made by Nelson Pass, the man, before Nakamichi gave Threshold a bad name and that drives Quads, Staxes, Sound Labs and whatever stators you throw at them beautifully...and it is more than 20 years old now and never saw a technician so far. I use it every time, one of my other amps decides to give up its ghost with excellent effect. It set me back $1800 at the time when I bought it. (I've just sold my Gryphon Referenes, which were just so so with stators, as well as all the Krell and Levinson stuff I auditioned with them, but I'll never part with that one. I love it.)