Brownian Sheet Images and Bessel-Riesz Capacity

关于具有循环长期记忆初始条件的随机分数Riesz-贝塞尔方程解的渐进行为

On asymptotic behavior of solutions to random fractional Riesz-Bessel equations with cyclic long memory initial conditions

本文研究了具有循环长期记忆初始条件的分数Riesz-贝塞尔方程的渐进行为，通过谱方法和渐进行为理论证明了解收敛于时空高斯随机场，并建立了多标度极限定理。

具有随机初始条件的分数阶Riesz-Bessel方程核平滑解的多尺度渐近分析

Multiscale Asymptotic Analysis of Kernel-Smoothed Solutions to Fractional Riesz-Bessel Equations with Random Initial Conditions

本文研究具有经典或循环长程依赖随机初始条件的分数阶Riesz-Bessel方程，通过核平滑方法获得非退化极限场，并证明其弱收敛到时空非平稳的高斯随机场。

Generalized dimensions of images of measures under Gaussian processes

We show that for certain Gaussian random processes and fields X:R^N to R^d, D_q(mu_X) = min{d, D_q(mu)/alpha} a.s. for an index alpha which depends on Holder properties and strong local nondeterminism of X, where q>1, where D_q denotes generalized q-dimension and where mu_X is the image of the measure mu under X. In particular this holds for index-alpha fractional Brownian motion, for fractional Riesz-Bessel motions and for certain infinity scale fractional Brownian motions.

所有正温度下库仑调制能量的均匀配分函数估计

Uniform Partition-Function Estimates for Coulomb Modulated Energy at All Positive Temperatures

该研究证明了所有正温度下三类核的中心调制能量的均匀配分函数估计，应用该估计得到了吉布斯测度的相关熵界、平均场收敛等结果，还确定了配分函数拉普拉斯变换的行列式表示及参数行为。

Infinite-dimensional stochastic differential equations and tail $ σ$-fields

We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs describe the dynamics of infinite-many Brownian particles moving in $ \mathbb{R}^d $ with free potential $ Φ$ and mutual interaction potential $ Ψ$. We apply the theorems to essentially all interaction potentials of Ruelle's class such as the Lennard-Jones 6-12 potential and Riesz potentials, and to logarithmic potentials appearing in random matrix theory. We …

高维渗流中的容量

Capacity in high dimensional percolation

本文在高维临界渗流中引入p-容量概念，证明其与初始无限团簇相交概率同阶，猜想与贝塞尔-里兹容量同阶，并给出单臂指数的简化证明。