Reuben Drogin (Yale)
Event Date
2026-09-22
Event Time
03:30 pm ~ 04:30 pm
Event Location
UPenn, 4C8 DRL
Random band matrices are Hermitian matrices with random entries supported in a band of width $W$ around the diagonal. The eigenfunctions of such matrices are expected to decay exponentially at the scale $W^2$ in dimension one, and $\exp(CW^2)$ in dimension two. Remarkably, the same scaling is expected for the cycle lengths in various models of random permutations where points are typically displaced by distances of order $W$. In this talk I will discuss some recent progress on these problems, some connections, and some open questions.