A short proof of Cramer's theorem in R

A calculus proof of the Cramér-Wold theorem

We present a short, elementary proof not involving Fourier transforms of the theorem of Cramér and Wold that a Borel probability measure is determined by its values on half-spaces.

Cramér定理的次指数版本

A subexponential version of Cramer's theorem

本文在次指数矩条件下研究独立同分布随机变量经验均值的大偏差，给出非凸且非Legendre-Fenchel变换导出的速率函数，并通过新的倾斜策略证明下界，推广了Cramér定理。

A short proof of the characterisation of convex order using the 2-Wasserstein distance

We provide a short proof of the intriguing characterisation of the convex order given by Wiesel and Zhang.

独立同分布随机变量下Feige猜想的简短证明

A short proof of Feige's conjecture for identically distributed random variables

针对独立同分布随机变量场景，本文给出Feige猜想的简短证明，为该猜想的验证提供了简洁方法。

弱无序相中有向聚合物扩散性的一个简短证明

A short proof of diffusivity for the directed polymers in the weak disorder phase

本文针对弱无序相中随机环境下的有向聚合物，给出了扩散性的一个新的简短初等证明。

Classical large deviations theorems on complete Riemannian manifolds

We generalize classical large deviations theorems to the setting of complete Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using visocity solutions for Hamilton-Jacobi equations. As a corollary, we also obtain the analogue of Cramér's theorem. The approach also provides a new proof of Schilder's theorem. Additionally, we provide a proof of Schilder's theorem by using an embedding into Euclidean space, together with Freidlin-Wentzell theory.