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math.PR2026
The oriented Kesten--McKay law for random regular digraphs
Yukun He, Jiaoyang Huang
We consider the adjacency matrix of a random directed -regular graph on vertices. For fixed , we prove that the empirical eigenvalue density converges in probabilit…
math.PR2026
Loop Equations Characterize Random Matrix Statistics
Paul Bourgade, Jiaoyang Huang
We prove that the universal local point processes of random matrix theory are characterized by their loop equation hierarchies. More precisely, for every rational , the $\math…
math.PR2026
Lecture Notes on Edge Universality for Random Regular Graphs
Jiaoyang Huang, Horng-Tzer Yau
The purpose of this note is to explain the structure, general strategy, and main ideas of the proof in the work of Huang, McKenzie, and Yau (2024) on the Ramanujan property and edg…