Invasive ground cover for compacted starved soil?

Straight over the road from me is a tree. It stands in a small rectangle of soil in the pavement. Nobody looks after that soil, and now very little grows in it (other than the tree). I'm sick of looking at it. I've seen some nice gardens and landscapes over the last week and they've kind of raised the bar a bit

If I was to accidentally spill a full packet of seeds on said ground, is there a particular type of seed that would result in very resilient, rampant, pretty ground cover?

 

I'm amazed the tree is still alive, google streetview shows it cut in half

 

This recent thread may have some suitable ideas. Gaz suggested epimedium - although I don't think you can grow that from seed.

http://gardenerscorner.co.uk/forum/threads/what-to-plant-around-sycamore-climbers-and-others.52037/

 

Try oxalis, the yellow flowered form is native and invasive, but you'll have to find some somewhere take piece and plant it there... In no time you'll have ground cover

 

If not try sedum, some are evergreen with nice flowers in summer... Erigeron maybe?