I'm a math PhD student. I've noticed that graduating students in top 5-10 schools, by the time they apply for postdocs, will regularly have several math research papers and several articles in preparation, usually with senior faculty. In contrast, at my (Research I university) PhD program most students will only graduate with 1 publication - their thesis. I came to graduate school with a solid knowledge of the "standard undergraduate math major curriculum" but no graduate courses, and no real idea of which adviser I wanted or what area of math, and I struggled to get to the current state of knowledge in a specific field. Looking back I don't see how it's possible for me to write several good papers during grad school. I just don't understand the phenomenon that I'm observing. I definitely think that I've worked hard. My guess is that most entering math grad students at top schools will have taken math graduate courses and will have already been reading research papers and know which research projects they want to work on - in other words, they are 2-3 years ahead of the game.
Question: Is there something fundamentally different about these top programs, independent of the knowledge, work ethic, etc. of the grad students, that makes creating an impressive publication record easier and/or more efficient? Is there some "secret"? What are the underlying mechanisms that allow students at Stanford or MIT to be so much more impressive on average than a student at a less prestigious place?