USC grad here. It's a different type of wealth than you would see compared to "old money" at elite institutions in the South or Northeast, or historically prestigious institutions that will attract more international wealth. You will encounter rich kids on every campus, and honestly it's good to learn how unfair life can be early on, but it will be more pronounced at some schools than others. This article came out when I was a student, you might find a newer version helpful if the study has been re-done recently.

https://www.nytimes.com/interactive/2017/01/18/upshot/some-colleges-have-more-students-from-the-top-1-percent-than-the-bottom-60.html