Can Vesta dominate the orbits of other asteroids? I think I remember a talk where a professor said that Vesta is a particularly important asteroid because its gravity is strong enough to perturb other asteroids.
In spite of Vesta's size, this effect might be so strong that some smaller asteroids might be kicked out of their orbits - making their way to Jupiter, or to the inner solar system.
Can Vesta dominate the orbits of other asteroids?
All related to the one question, there are particular points I'm interested in:


*

*if so, how often, presumably?

*is there a preferred direction (inwards / outwards)? 

*has the perturbation rate been constant over geologic timescales?

*do the "victims" stay in the plane of the ecliptic? 

*did someone model such processes?


I currently think the whole process is chaotic - essentially unpredictable. 
 A: Vesta is a very large asteroid ~ 530 Km in diameter, the third largest in the Solar System (and second most massive). Ceres is the largest, and is considered a Dwarf Planet (~ 900 Km diameter). Vesta is in the plane of the Solar System (like all the major planets) and behaves very much like a good citizen of the Solar System, obeying Kepler's Laws.
You're right that Chaos is involved. The term Chaos Theory describes the delicate balance which some things sit in if they have multiple significant, competing and regular forces acting on them. For small asteroids this the regular pull from Jupiter, the Sun (both massive but far away) and big neighbours (like Ceres and Vesta, who are less massive but much closer).
Everything in the Solar System will orbit the Sun periodically (and mostly predictably), unless perturbed. For the big planets this isn't too much of a problem. However, on occasion the gravitational pull on small asteroids, from the Sun, Jupiter and massive asteroids will be significant. If gravitational forces and small asteroid momentum are competing (e.g. in different directions), the asteroid can enter into a chaotic regime and whizz around erratically. Mostly these regimes are short-lived and the small asteroid will settle into a new orbit (which may or may not suffer more of these jitters into chaotic regimes).
If you knew where all the asteroids were, you could in principle calculate which small asteroids would pass into chaotic regimes. You could not predict where or on what orbits these small asteroids would end up. These sorts of interactions can happen at any time, so on human and not geological timescales.
A: Ceres is the most important asteroid, having over half the mass of the entire asteroid belt. Vesta is the third largest, and smallest one to have enough gravity to crunch into a spherical shape.
Any time two bodies collide or, if they are large enough to have significant gravity, nearly collide, they are going to change their direction of travel. Typically, both bodies after a collision will have less energy than they did before, some having been dissipated into heat by the process of deformation. At most, you would only expect a little more energy in the smaller one. By orbital mechanics, that means that they are probably going to go from nice, nearly circular orbits to something more elliptical, with the long axis of the ellipse smaller than the previous radius. Towards the Sun, broadly speaking, is downhill in the Solar System, and away from the Sun is uphill.
Since objects in orbit are traveling pretty fast, and their relative speed, that is, the speed of collision, is small in comparison, they will probably mostly stay on their previous courses, so they will probably not be knocked very far out of the ecliptic.
You would need to know the position of a huge number of objects to fantastic precision to be able to predict the collision of small bodies very far in the future, so in that sense it is chaotic.
Bodies collided alllllll the time in the early history of the Solar System, but by now most of the collisions that were gonna happen, have happened. They are relatively sparse now. And yes, there are lots of people modeling planetary formation.
