Things can't really "leave", well they can, but the best guess we have is that there is no particularly special place in the universe, everywhere is roughly the same. So if even if all the really speedy stuff from here "left" we'd see the speedy stuff arriving from other places.

I thought 'no special place' was meant to say physics was the same everywhere; not the environment.

If you have a sparse gas with a random distribution of velocities and you let it sit for a while, you will find that the outliers on the upper end have have moved further away from cluster center. They have boiled off.

The point is that as far as we can tell there isn't a "center" of the universe.

Try simulating this: Start with bunch of objects at coordinates 0,0,0. Give them random velocities from 0 to c. Then just let them move according to Newtons laws of motion, ignore gravity.

Now focus on single random object and narrow down your field of view so you won't see the edge. Look at other objects. They will seem to be moving away directly from the point you focused on with velocities proportional to distance from it.

I made such simulation and calculated that the relative velocities of other points face directly away from the point I'm observing. And they really do.

There's definitely a center of this system, yet from the point of view of any object far enough from the edge to not be able to see it, it seems like there's no center and other objects just move away from us, and from each other with speed proportional to the distance.

But in that model you would not see a uniform distribution of objects within your field of view. It's observably anisotropic, while we observe the universe to be isotropic.

In that model if you can't see the edge because you are far enough from it the distribution you observe is exactly isotropic regardless of which object you choose as your point of view.

Same way that you can't figure out where the center is, you can't figure any special direction or plane.

Try sumulating this model yourself. Everything looks exactly as if you were in the center of Big Bang, even when you are not.

Because it is an open set?

On average though, you'll find similar outliers in whatever direction you look.

Not really if the initial speeds were random from 0 to c. Some stuff would leave but some would stay relatively close.

And you wouldn't be able to tell what's your speed when you look at how other stuff moves. Everythin would look like moving away from you with speed proportional to the distance.