Kexin Yu

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math.PR2026

Large corank of dense random regular digraphs

Huaijin Liang, Kexin Yu, Tingzhou Yu

Let $1 \leq k \leq n$ and let $A$ be the adjacency matrix of a uniformly random $d$ -regular directed graph on $n$ vertices. Suppose that $λn \leq d \leq (1 - λ) n$ for a fixed $0 < λ \leq 1/2$ .…

math.PR2026

Rank and Invertibility of Dense Signed Random Regular Matrices

Huaijin Liang, Yuxiao Shi, Kexin Yu +1

Let $A$ be the (non-symmetric) adjacency matrix of a uniformly random $d$ -regular directed graph on $n$ vertices, and let $Ξ$ be independent of $A$ with i.i.d. Rademacher entries.…

math.PR2025

The smallest singular value of sparse discrete random matrices

Kexin Yu

Let $M_{n}$ be an $n \times n$ random matrix with i.i.d. sparse discrete entries. In this paper, we develop a simple framework to solve the approximate Spielman-Teng theorem for $M_n…