Will a new planet form if Jupiter's influence on asteroid belt will diminish in a few billion years?
Sometime after 4.5 billion years, the sun will change into a red giant star and expand to about 1 AU. Some people think it will be beyond Earth's orbit. (In any case, Earth's orbit would have changed and likely to have struck the surface of the expanded sun.) The asteroids would experience a stronger solar wind and their orbits would become more elliptical, so Jupiter's influence would be significant.