Quasipotential and logarithmic asymptotics of the Green's measures

带对数奇点的Gaussian自由场与约化格林能量

Gaussian free field with logarithmic singularities and reduced Green's energy

本文研究多边形域中带对数奇点的Gaussian自由场的水平线，证明其分布与无奇点情形绝对连续，导数由约化格林能量给出，并揭示奇点附近行为的显著差异。

Asymptotic entropy and green speed for random walks on countable groups

We study asymptotic properties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjamini and Peres [Probab. Theory Related Fields 98 (1994) 91--112]), we give an alternative proof relying on a version of the so-called fundamental inequality (relating the rate of escape, the entropy and th…

球系综及其扩展的奇异中心极限定理

Singular central limit theorems for the spherical ensemble and beyond

研究球系综中对数格林奇异性的波动，发现光滑可观测量具有通常的Sobolev或高斯自由场波动，而对数奇异性在更大对数尺度上渐近解耦，产生显式白噪声极限。