>A snow ball rolling down a mountain
It's surface area gets bigger, thus the ball collects more snow until it can't hold it's own weight anymore.
>Two hot dog stands are next to each other
If one has a substantially bigger line than the other and you know nothing about any of the stands, you'll pick the one that's more corwded because that probably means it's better. That is, until you reach a line so long that makes you pick the other.
>The richer get richer, the poorer get poorer
People with higher levels on income can get better positions through upper class networking while people with low income more often than not are offered low paying positions. This process doesn't seem to reach equilibrium in the short term, unlike the other two.

There should be an explanation for this, are these examples part of a bigger set of problems? Which branch of math deals with these type of stuff? My best guess would be statistics but I think it may go deeper than that.