Tian-Le Liu

collaborators

2 papers

math.PR2026

Universal Beta Incidence Angles: Cauchy Rigidity and Infinite Arrangements

Tianle Liu

Let $U$ be Haar-uniform on $S^{p - 1}$ , let $a_{1}, \dots, a_{k}$ be arbitrary nonzero vectors, and let $w_{1}, \dots, w_{k}$ be simplex weights. Define \[ g(U)=\sum_{j=1}^k w_j\frac{a…

math.PR2026

Kac's Walk on Rotation Matrices Mixes in $Θ (n^{2})$ Steps: A Proof Discovered with AI

Tianle Liu

Let $N = (2 n) = dim SO (n)$ . We prove that the coordinate-plane Kac walk on $SO (n)$ has total-variation mixing time of order $N$ : for every fixed $0<\varepsilon<1…

Universal Beta Incidence Angles: Cauchy Rigidity and Infinite Arrangements

Kac's Walk on Rotation Matrices Mixes in Θ(n2) Steps: A Proof Discovered with AI

Kac's Walk on Rotation Matrices Mixes in $Θ (n^{2})$ Steps: A Proof Discovered with AI