Big stacks can loosen up and play more aggressively against the short stacks because
a) if the short stacks are playing tight and they're in push/fold mode, big stack can put a lot of pressure on them to make a big decision for the tournament.
b) there is no fear of busting if you do run into a hand against the short stack. this is because of your stack size and be, you still have a lot of equity against short stack shove ranges if you call if you're call range is very wide.
Players are slightly more fearful because just because there is the threat of busting out of a tournament when playing against them. Even with premium hands like AKs, QQ+. Now, I don't think you should fear getting your money in with these hands, but there's always the chance big stack will hit and bust you. Again, large stacks don't worry about that.
Large stacks don't necessarily have to raise you all in to apply pressure. They can make standard 3x bets against a player on a 10BB stack and that's enough. Flatting is costing 30% of the stack, min raising commits you to the pot and you're calling any shove, and if you shove the big stack could easily call you. So, you're in a bit of a predicament of what to do unless you have a strong hand. This is even more true if you're near a the money bubble and you're a player who wants to at least cash in, now you're even more likely to fold a ton of your hands just to secure a money spot.
I don't think there is a mathematical explanation of big stacks having a greater likelihood of growing than small stacks. Big stacks can call a preflop raises with larger range of hands to try and hit flops hard. For example, lets say MP with 35BBs raised it 3x BB with A10o, it's folded to the BTN with 100BBs who calls with Q6s to try and hit a good flop. They can do this because it's not costing them a large percent of their stack and if they miss they can fold and if they hit, they're getting paid off. Or even if they do miss, they can apply pressure and steal the pot. Short stacks can't do this because a call with weak hands like Q6s is costing too much of their stack to call and try to hit a flop. So, big stacks can take more risk with mediocre hands to try and build big pots while short stacks can't.