Now if there is "more space" around particle A, particle B will have a slightly higher statistical chance of randomly jumping closer to it, than farther.
Rinse-repeat. Gravity as we know it.
Does it? A single free particle won't "jump around randomly". Thermal motion is plain Newtonian motion with an extremely high rate of collisions. There's nothing random about it (let's put quantum things aside for now).
Why?
Also how do you explain acceleration due to gravity with that model. How do you explain solid objects?
Repeating results in movement, getting closer to the object intensifies this effect, results in acceleration.
Solid objects are products of electric charge preventing atoms/particles from hitting each other, I dont think that has to have to do anything with gravity in this example?
E.g. if we have earth and moon:
O o
Like if you dropped the earth on a giant sheet, it would stretch the sheet more than what the moon would have.
Would this imply that cold objects have weaker gravity?
rest mass = all the energies of the mass, not just its thermal energy. So, as it approaches 0 kelvin the thermal energy approaches 0 and the mass approaches its minimal possible energy (its kinetic energy approaches zero), but even at absolute zero, it still has the rest-mass of its fundamental particles (electrons, neutrons and protons) which have mass inherently. In practice, the scale of the mass of the particles massively outweighs the scale of the thermal mass, so while strictly true, it mostly doesn't matter.
So, because the scaling factor is stupid stupid large, changing temperature from anything to absolute zero does lower the mass, which does lower the gravity, but it just doesn't matter.