Author

Shuang Sun

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Preprint Oct 2026

A Proof of the Erd\H{o}s Matching Conjecture for Large Matchings via Sharp Tail Probability for Sums of i.i.d. Nonnegative Random Variables

We resolve a conjecture of \L{}uczak, Mieczkowska and \v{S}ileikis on the maximal tail probability of sums of independent and identically distributed nonnegative random variables. Specifically, for every integer $k\ge1$ and every $0\le x\le1/k$, we prove \[ \sup_{\mathbb E X_1\le x}\mathbb{P}(X_1+\cdots+X_k\ge1) =\max\...

Cheng Chi, Shuang Sun, Yan Wang · 0 citations

Preprint Sep 2026

Sharp edge-spectral supersaturation for odd cycles

Let $G$ be a graph with $m$ edges and adjacency spectral radius$\rho(G)$, and let $N(C_{2k+1},G)$ denote the number of copies of $C_{2k+1}$ in $G$. For each fixed integer $k\ge 2$, define $ g_k(m):=\frac{k-1+\sqrt{4m-k^2+1}}{2}. $ Li, Zhai and Shu [European J. Combin., 2024] determined the spectral extr...

Jia-Qi Liu, Zhenzhen Lou, Shuang Sun · 1 citation

Preprint Jul 2026

Asymptotic Uniformity of Permanents of Random Matrices over Finite Fields of Odd Characteristic

Let $q$ be an odd prime power, and let $A_n=(a_{ij})\in\mathbb F_q^{n\times n}$ be a random matrix whose entries are independent and uniformly distributed on $\mathbb F_q$. The permanent of $A_n$ is defined by $\operatorname{per}(A_n)=\sum_{\sigma\in S_n}\prod_{i=1}^n a_{i,\sigma(i)}$, where $S_n$ denotes the symmetric...

Shuang Sun, Yuyao Yang, Ji Zeng · 0 citations