기초과학연구원 이산수학그룹
On December 8, 2025, Matthew Kwan from ISTA, Austria, gave a talk at the Discrete Math Seminar on the permanent of a random ±1-matrix. The title of his talk was “Exponential anticoncentration of the permanent“.
Let A be a random n×n matrix with independent entries, and suppose that the entries are “uniformly anticoncentrated” (for example, A could be a uniformly random n×n matrix with ±1 entries). We prove that the permanent of A is exponentially anticoncentrated, significantly improving previous bounds of Tao and Vu. Our proof also works for the determinant, giving an alternative proof of a classical theorem of Kahn, Komlós and Szemerédi. Joint work with Zach Hunter and Lisa Sauermann.