Probability and Mathematical Physics Seminar

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Localization for Quantum and Classical models in One Dimension

Speaker: Reuben Drogin, Yale University

Location: Warren Weaver Hall 1302

Date: Friday, February 27, 2026, 11:10 a.m.

Synopsis:

Random band matrices (RBMs) are Hermitian matrices with random entries supported in a band of width W around the diagonal. The eigenfunctions of such matrices are expected to exponentially decay at the scale W^2 in dimension one, and exp(CW^2) in dimension two. The same scaling is expected for the cycle lengths in various models of random permutations in which points are typically displaced by distances of order W. In this talk I will discuss some aspects of the proof of this conjecture for RBMs in dimension one, and progress, joint with Felipe Hernández, on the analogous conjecture for random permutations in dimension one.