TITLE: Is residual finiteness a property of "many" finitely presented groups?
QUESTION [8 upvotes]: Is there a reasonable random model for selecting a finitely presented group $G$ such that with positive probablity (or even with probability almost $1$) some of the following properties hold:

$G$ is residually finite.
$G$ is subgroup seperable (LERF).
The first $l_2$ Betti number of $G$ is positive.
The cost of $G$ is greater than 1.

REPLY [4 votes]: A random group at density less than 1/6 is known to be the fundamental group of a compact, non-positively curved cube complex, by Ollivier--Wise.  By Agol's theorem, all such hyperbolic groups are virtually special, and hence residually finite, QCERF, etc.