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Yahui Qu

Publications and source records attributed to Yahui Qu.

3 recordsLinked to original sources
arXiv2026

Scaling limit of the 3D abelian Yang--Mills Langevin dynamics

We study the continuum scaling limit of the Langevin dynamics for three-dimensional U(1) lattice Yang--Mills theory. The model is defined on the discrete 3D torus with a general class of plaquette actions that are suitably normalized, including Wilson, Manton, and Villain actions. Under the weak-coupling scaling and in the DeTurck gauge, we prove that, locally in time and in probability, the rescaled logarithmic field converges to the solution of the one-form stochastic heat equation. In particular, the limiting dynamics are universal and do not depend on the higher-order details of the plaquette action.

math.PR↗
arXiv2026

The pair correlation function of the Sine$_6$ process

We derive an explicit formula for the pair correlation function of the Sine$_6$ process in terms of Bessel functions of the first kind. This provides the first single-variable special function representation of the pair correlation function for the bulk limit of a beta-ensemble beyond the classical values of $\beta=1,2,$ and $4$.

math.PR↗
arXiv2025

On the pair correlation function of the Sine$_\beta$ process

We study the Sine$_\beta$ process, the bulk point process scaling limit of beta-ensembles. We provide a representation of its pair correlation function for all $\beta>0$ via a stochastic differential equation. We show that the pair correlation function is continuous in $\beta$, and provide estimates for its asymptotic decay. We recover the classical explicit formula for the pair correlation function in the $\beta=2$ and $4$ cases. For $\beta=2n$, we derive the power series expansion of the pair correlation function, and express it in terms of a size $n$ linear ordinary differential equation system. We obtain our results by studying the density of the $\operatorname{HP}_{\beta,\delta}$ process, the point process limit of the circular Jacobi beta-ensembles.

math.PR↗