After thinking about it a bit more and realizing I answered
the wrong question.... ;-)
If you need to move the particle to create some space, for
mathematical purposes you can assume each instance is a sphere whose radius is
equal to the min distance you're willing to accept and compute artificial
surface normals to use as a direction vector to offset the emitted
particle. That is, if a particle gets too close to an object, find the
object's artificial surface normal and use that vector to push the particle away
from it.
Another route that I remember Olivier suggesting a few
years ago to address a different problem: start with a uniform grid or other
shape, then emit particles from the vertices varying their positions to the
desired degree of randomness. This will give you some control over
placement while retaining the random nature.
Matt