Jiahe Shen

activity

20242026

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3 papers · 1 filter

math.CO2025

The Szemerédi-Trotter theorem over arbitrary field of characteristic zero

Jiahe Shen

Let $P$ be a set of $m$ points and $L$ a set of $n$ lines in $K^{2}$ , where $K$ is a field with char $(K) = 0$ . We prove the incidence bound $$\mathcal{I}(\mathcal{P…

math.PR2025

Universality of rational canonical form for random matrices over a finite field

Jiahe Shen

In this note, we study the distribution of the rational canonical form of a random matrix over the finite field $F_{p}$ , whose entries are independent and $ε$ -balanced with…

math.PR2025

Gaussian Universality of Products Over Split Reductive Groups and the Satake Isomorphism

Jiahe Shen

We establish that the singular numbers (arising from Cartan decomposition) and corners (emerging from Iwasawa decomposition) in split reductive groups over non-archimedean fields a…