X. Han

activity

20232025

collaborators

6 papers

math.PR2025

A few observations around Gaussian domination and continuous symmetry breaking for spin O(N) model

Xiao Han

We investigate the notion of Gaussian domination for the spin $O (N)$ model on general finite graphs. We begin by proving a general inequality for spin correlations under the assump…

math.GT2025

Nearly geodesic surfaces are filling

Xiaolong Hans Han

Let $M$ be a closed hyperbolic $3$ -manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$ . We prove that…

math.CA2024

The semiclassical measure of certain spherical harmonics on S3

Xiaolong Han

Bourgain used the Rudin-Shapiro sequences to construct a basis of uniformly bounded holomorphic functions on the unit sphere in C2. They are also spherical harmonics (i.e., Laplaci…

math.CA2024

Fractal uncertainty principle for random Cantor sets

Xiaolong Han, Pouria Salekani

We continue our investigation of the fractal uncertainty principle (FUP) for random fractal sets. In the prequel (arXiv:2107.08276), we considered the Cantor sets in the discrete s…

math.CO2023

A new bound for the Fourier-Entropy-Influence conjecture

Xiao Han

In this paper, we prove that the Fourier entropy of an $n$ -dimensional boolean function $f$ can be upper-bounded by $O (I (f) + k \in [n] \sum I_{k} (f) lo g \frac{1}{I _{k} ( f )})$ , whe…

math.GT2023

Thurston norms, $L^{2}$ -norms, geodesic laminations, and Lipschitz maps