Is there any result that relates the minimum degree of a geometric random graph to its k-vertex connectivity? I read papers where they pose the condition $$d\_{\rm min} \geq k$$
to imply that the graph is k-connected (vertex connectivity). Is that an approximation or an asymptotic result? In my case, I need, if not an exact result, a lower bound 


$$P({\rm graph~is~connected}) \geq f(d\_{\rm min}).$$


I could not find references so far.



$k$-connectivity of a geometric random graph
Does this help?
<http://www.maths.bath.ac.uk/~masmdp/ab/kcon.html>


