Conformal Deformation from Normal to Hermitian Random Matrix Ensembles

非对称稀疏随机矩阵有限秩加性变形的极值特征值和特征向量

Extreme eigenvalues and eigenvectors for finite rank additive deformations of non-hermitian sparse random matrices

研究非对称稀疏随机矩阵在有限秩加性变形下的极值特征值和特征向量行为，证明其与变形矩阵的特征值渐近一致，并揭示了秩一变形下的投影行为与厄密情况相同。

Double dimers, conformal loop ensembles and isomonodromic deformations

The double-dimer model consists in superimposing two independent, identically distributed perfect matchings on a planar graph, which produces an ensemble of non-intersecting loops. Kenyon established conformal invariance in the small mesh limit by considering topological observables of the model parameterized by $\SL_2(\C)$ representations of the fundamental group of the punctured domain. The scaling limit is conjectured to be $\CLE_4$, the Conformal Loop Ensemble at $κ=4$. In support of this conjecture, we prove that a large subclass of these topological correlators converge to their putative…

Large deviations for the largest eigenvalue of an Hermitian Brownian motion

We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE.